diff --git a/content/lessons/quant/quant-arithmetic-exponents-roots.md b/content/lessons/quant/quant-arithmetic-exponents-roots.md
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+---
+id: quant-arithmetic-exponents-roots
+section: quant
+topic: arithmetic
+subtopic: exponents-roots
+title: "Exponents & Roots"
+tags: [exponents, roots, radicals, powers]
+author: openmat
+reviewers: []
+status: in-review
+original: true
+license: CC-BY-SA-4.0
+---
+
+## Overview
+
+Exponents and roots show up all over GMAT Focus Quant — inside number-properties questions, in
+disguised equations, and as the fast way to compare very large or very small quantities. Almost
+everything reduces to a short list of rules plus one habit: **rewrite every base as a power of the
+same prime before you do anything else.**
+
+## Core concepts
+
+**The exponent rules.** For any nonzero base and integer (or rational) exponents:
+
+- Product: \(a^m \cdot a^n = a^{m+n}\) — same base, *add* exponents.
+- Quotient: \(\dfrac{a^m}{a^n} = a^{m-n}\) — same base, *subtract* exponents.
+- Power of a power: \((a^m)^n = a^{mn}\) — *multiply* exponents.
+- Distributes over products: \((ab)^n = a^n b^n\).
+
+**Zero and negative exponents.**
+
+\[a^0 = 1 \quad (a \ne 0), \qquad a^{-n} = \frac{1}{a^n}\]
+
+A negative exponent means "reciprocal," not "negative number." So \(2^{-2} = \tfrac14\), which is
+positive.
+
+**Roots are fractional exponents.** This is the single most useful bridge:
+
+\[\sqrt[n]{a} = a^{1/n}, \qquad a^{m/n} = \left(\sqrt[n]{a}\right)^m = \sqrt[n]{a^m}\]
+
+So \(27^{2/3} = \left(27^{1/3}\right)^2 = 3^2 = 9\). Take the root first (smaller numbers), then the power.
+
+**Simplifying radicals.** Pull perfect-square factors out from under a square root, and combine only
+*like* radicals:
+
+\[\sqrt{ab} = \sqrt{a}\,\sqrt{b}, \qquad \sqrt{50} = \sqrt{25\cdot 2} = 5\sqrt{2}\]
+
+You can add \(5\sqrt2 + 3\sqrt2 = 8\sqrt2\), but you **cannot** turn \(\sqrt2 + \sqrt2\) into
+\(\sqrt4\).
+
+**Same-base strategy for equations.** When an equation has different bases that are all powers of one
+prime, rewrite them and set the exponents equal:
+
+\[4^{x+1} = 8^{x-1} \;\Rightarrow\; 2^{2(x+1)} = 2^{3(x-1)} \;\Rightarrow\; 2x+2 = 3x-3 \;\Rightarrow\; x = 5\]
+
+## Worked examples
+
+**Combine rules.** Simplify \((x^2)^3 \cdot x^4\). Power of a power gives \(x^{6}\); then the product
+rule adds exponents: \(x^{6} \cdot x^{4} = x^{10}\).
+
+**Fractional exponent.** Evaluate \(27^{2/3}\). Cube root of 27 is 3; square it: \(3^2 = 9\).
+
+**Radicals.** Simplify \(\sqrt{50} + \sqrt{18} = 5\sqrt2 + 3\sqrt2 = 8\sqrt2\).
+
+## Common traps
+
+- **Multiplying exponents when you should add.** \(2^5 \cdot 2^3 = 2^{8}\), not \(2^{15}\). You only
+  multiply exponents for a *power of a power*, \((2^5)^3 = 2^{15}\).
+- **Negative exponent → negative number.** \(3^{-1} = \tfrac13\), a positive fraction, not \(-3\).
+- **Adding under the radical.** \(\sqrt{a} + \sqrt{b} \ne \sqrt{a+b}\). \(\sqrt{9} + \sqrt{16} = 3+4 = 7\), not \(\sqrt{25} = 5\).
+- **Combining unlike bases.** \(2^3 \cdot 3^3\) is \((2\cdot3)^3 = 6^3\), but \(2^3 \cdot 3^2\) cannot be merged into one base.
+
+## Key takeaways
+
+- Same base: add exponents to multiply, subtract to divide, multiply to raise a power to a power.
+- \(a^0 = 1\) and \(a^{-n} = 1/a^n\); negative exponents give positive reciprocals.
+- Roots are fractional exponents: \(a^{m/n} = \sqrt[n]{a^m}\) — take the root first, then the power.
+- To solve exponential equations, rewrite every base as the same prime and equate the exponents.
diff --git a/content/questions/quant/quant-arithmetic-exponents-roots-0017.md b/content/questions/quant/quant-arithmetic-exponents-roots-0017.md
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+---
+id: quant-arithmetic-exponents-roots-0017
+section: quant
+topic: arithmetic
+subtopic: exponents-roots
+type: problem-solving
+difficulty: easy
+tags: [exponents, quotient-rule]
+choices:
+  A: "5"
+  B: "25"
+  C: "125"
+  D: "625"
+  E: "5^{11}"
+answer: C
+author: openmat
+reviewers: []
+status: in-review
+original: true
+license: CC-BY-SA-4.0
+---
+
+## Question
+
+What is the value of \(\dfrac{5^{7}}{5^{4}}\)?
+
+## Explanation
+
+Same base, division — **subtract** the exponents:
+
+\[\frac{5^{7}}{5^{4}} = 5^{7-4} = 5^{3} = 125\]
+
+The answer is **125**.
+
+**The traps:** choice **E** (\(5^{11}\)) *adds* the exponents, which is the rule for
+*multiplication*, not division. Choices that divide the exponents (\(7 \div 4\)) or cancel bases
+incorrectly land on the smaller powers of 5.
+
+## Hints
+
+- Same base with division: what do you do to the exponents?
+- \(5^{7} / 5^{4} = 5^{7-4}\). Now just evaluate the small power.
diff --git a/content/questions/quant/quant-arithmetic-exponents-roots-0018.md b/content/questions/quant/quant-arithmetic-exponents-roots-0018.md
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+---
+id: quant-arithmetic-exponents-roots-0018
+section: quant
+topic: arithmetic
+subtopic: exponents-roots
+type: problem-solving
+difficulty: easy
+tags: [exponents, zero-exponent, negative-exponent]
+choices:
+  A: "0"
+  B: "1"
+  C: "1.25"
+  D: "1.5"
+  E: "9"
+answer: C
+author: openmat
+reviewers: []
+status: in-review
+original: true
+license: CC-BY-SA-4.0
+---
+
+## Question
+
+What is the value of \(7^{0} + 2^{-2}\)?
+
+## Explanation
+
+Handle each term with the definitions of the zero and negative exponents:
+
+\[7^{0} = 1, \qquad 2^{-2} = \frac{1}{2^{2}} = \frac{1}{4}\]
+
+So the sum is
+
+\[1 + \frac{1}{4} = \frac{5}{4} = 1.25\]
+
+The answer is **1.25**.
+
+**The traps:** choice **A (0)** assumes \(7^0 = 0\), but any nonzero base to the zero power is 1.
+Choice **E (9)** reads \(2^{-2}\) as \(-2\times 2\) or \(2^2\) plus a sign slip — a negative exponent
+gives a positive *reciprocal*, not a negative number.
+
+## Hints
+
+- Any nonzero number raised to the power 0 equals 1 — not 0.
+- A negative exponent means take the reciprocal: \(2^{-2} = 1/2^{2}\), a positive fraction.
diff --git a/content/questions/quant/quant-arithmetic-exponents-roots-0019.md b/content/questions/quant/quant-arithmetic-exponents-roots-0019.md
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+---
+id: quant-arithmetic-exponents-roots-0019
+section: quant
+topic: arithmetic
+subtopic: exponents-roots
+type: problem-solving
+difficulty: medium
+tags: [exponents, power-of-a-power, product-rule, variables]
+choices:
+  A: "x^{9}"
+  B: "x^{10}"
+  C: "x^{12}"
+  D: "x^{14}"
+  E: "x^{24}"
+answer: B
+author: openmat
+reviewers: []
+status: in-review
+original: true
+license: CC-BY-SA-4.0
+---
+
+## Question
+
+For \(x \neq 0\), which of the following is equal to \(\left(x^{2}\right)^{3} \cdot x^{4}\)?
+
+## Explanation
+
+Apply the rules in order. First, **power of a power** — multiply the exponents:
+
+\[\left(x^{2}\right)^{3} = x^{2\cdot 3} = x^{6}\]
+
+Then the **product rule** — same base, add the exponents:
+
+\[x^{6} \cdot x^{4} = x^{6+4} = x^{10}\]
+
+The answer is **\(x^{10}\)**.
+
+**The traps:** choice **E** (\(x^{24}\)) multiplies all three exponents (\(2\cdot 3\cdot 4\)) as if
+everything were a power of a power. Choice **A** (\(x^{9}\)) adds \(2+3+4\), mixing up which
+operation adds and which multiplies. Multiply for a power raised to a power; add when multiplying
+like bases.
+
+## Hints
+
+- Do the inner operation first: \((x^2)^3\) is a power raised to a power.
+- Once you have a single power of \(x\) times another, add those two exponents.
diff --git a/content/questions/quant/quant-arithmetic-exponents-roots-0020.md b/content/questions/quant/quant-arithmetic-exponents-roots-0020.md
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@@ -0,0 +1,46 @@
+---
+id: quant-arithmetic-exponents-roots-0020
+section: quant
+topic: arithmetic
+subtopic: exponents-roots
+type: problem-solving
+difficulty: medium
+tags: [roots, radicals, simplifying-radicals]
+choices:
+  A: "\\sqrt{68}"
+  B: "2\\sqrt{17}"
+  C: "8\\sqrt{2}"
+  D: "15\\sqrt{2}"
+  E: "34"
+answer: C
+author: openmat
+reviewers: []
+status: in-review
+original: true
+license: CC-BY-SA-4.0
+---
+
+## Question
+
+What is \(\sqrt{50} + \sqrt{18}\) in simplest form?
+
+## Explanation
+
+Pull the perfect-square factor out of each radical, then combine the *like* radicals:
+
+\[\sqrt{50} = \sqrt{25 \cdot 2} = 5\sqrt{2}, \qquad \sqrt{18} = \sqrt{9 \cdot 2} = 3\sqrt{2}\]
+
+Both are multiples of \(\sqrt2\), so add the coefficients:
+
+\[5\sqrt{2} + 3\sqrt{2} = 8\sqrt{2}\]
+
+The answer is **\(8\sqrt{2}\)**.
+
+**The traps:** choice **A** (\(\sqrt{68}\)) adds *under* the radical (\(50+18\)), but
+\(\sqrt{a} + \sqrt{b} \neq \sqrt{a+b}\). Choice **D** (\(15\sqrt2\)) multiplies the coefficients
+instead of adding them. You may add radicals only when the parts under the root already match.
+
+## Hints
+
+- Factor out the largest perfect square from each radical first.
+- After simplifying, both terms are multiples of \(\sqrt2\). Add only the numbers in front.
diff --git a/content/questions/quant/quant-arithmetic-exponents-roots-0021.md b/content/questions/quant/quant-arithmetic-exponents-roots-0021.md
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@@ -0,0 +1,43 @@
+---
+id: quant-arithmetic-exponents-roots-0021
+section: quant
+topic: arithmetic
+subtopic: exponents-roots
+type: problem-solving
+difficulty: medium
+tags: [exponents, fractional-exponents, roots]
+choices:
+  A: "6"
+  B: "9"
+  C: "18"
+  D: "81"
+  E: "729"
+answer: B
+author: openmat
+reviewers: []
+status: in-review
+original: true
+license: CC-BY-SA-4.0
+---
+
+## Question
+
+What is the value of \(27^{2/3}\)?
+
+## Explanation
+
+A fractional exponent combines a root and a power: the denominator is the root, the numerator is the
+power. Take the root **first** to keep the numbers small:
+
+\[27^{2/3} = \left(27^{1/3}\right)^{2} = \left(\sqrt[3]{27}\right)^{2} = 3^{2} = 9\]
+
+The answer is **9**.
+
+**The traps:** choice **E** (\(729 = 27^2\)) ignores the cube root entirely. Choice **C (18)**
+multiplies the base by the exponent (\(27 \times \tfrac23\)). Choice **A (6)** takes the cube root
+but then multiplies by 2 instead of squaring.
+
+## Hints
+
+- Rewrite the exponent as a root and a power: the bottom of the fraction is the root.
+- Cube root of 27 is a small number — find it first, then apply the remaining power.
diff --git a/content/questions/quant/quant-arithmetic-exponents-roots-0022.md b/content/questions/quant/quant-arithmetic-exponents-roots-0022.md
new file mode 100644
index 0000000..03d9e31
--- /dev/null
+++ b/content/questions/quant/quant-arithmetic-exponents-roots-0022.md
@@ -0,0 +1,49 @@
+---
+id: quant-arithmetic-exponents-roots-0022
+section: quant
+topic: arithmetic
+subtopic: exponents-roots
+type: problem-solving
+difficulty: hard
+tags: [exponents, exponential-equations, same-base]
+choices:
+  A: "2"
+  B: "3"
+  C: "4"
+  D: "5"
+  E: "7"
+answer: D
+author: openmat
+reviewers: []
+status: in-review
+original: true
+license: CC-BY-SA-4.0
+---
+
+## Question
+
+If \(4^{x+1} = 8^{x-1}\), what is the value of \(x\)?
+
+## Explanation
+
+The bases 4 and 8 are both powers of 2, so rewrite everything with base 2:
+
+\[4^{x+1} = \left(2^{2}\right)^{x+1} = 2^{2(x+1)}, \qquad 8^{x-1} = \left(2^{3}\right)^{x-1} = 2^{3(x-1)}\]
+
+With a common base, the exponents must be equal:
+
+\[2(x+1) = 3(x-1)\]
+\[2x + 2 = 3x - 3\]
+\[x = 5\]
+
+The answer is **5**.
+
+**Check:** \(4^{6} = 4096\) and \(8^{4} = 4096\). ✓
+
+**The trap:** trying to compare 4 and 8 directly, or guessing a small value, misses the key move —
+express both sides as powers of the same prime, then set the exponents equal.
+
+## Hints
+
+- Both 4 and 8 are powers of 2. Rewrite each side with base 2.
+- Once the bases match, the exponents must be equal — solve the resulting linear equation.
diff --git a/docs/data/content.json b/docs/data/content.json
index 9ef981c..c53a749 100644
--- a/docs/data/content.json
+++ b/docs/data/content.json
@@ -7,8 +7,8 @@
   "stats": {
     "quant": {
       "label": "Quantitative",
-      "questions": 16,
-      "lessons": 5
+      "questions": 22,
+      "lessons": 6
     },
     "verbal": {
       "label": "Verbal",
@@ -22,8 +22,8 @@
     }
   },
   "counts": {
-    "questions": 32,
-    "lessons": 8
+    "questions": 38,
+    "lessons": 9
   },
   "questions": [
     {
@@ -301,6 +301,186 @@
         "Or use the coefficient shortcut: sum of roots \\(= -b\\), product \\(= c\\)."
       ]
     },
+    {
+      "id": "quant-arithmetic-exponents-roots-0017",
+      "section": "quant",
+      "topic": "arithmetic",
+      "subtopic": "exponents-roots",
+      "type": "problem-solving",
+      "difficulty": "easy",
+      "tags": [
+        "exponents",
+        "quotient-rule"
+      ],
+      "choices": {
+        "A": "5",
+        "B": "25",
+        "C": "125",
+        "D": "625",
+        "E": "5^{11}"
+      },
+      "answer": "C",
+      "author": "openmat",
+      "reviewers": [],
+      "status": "in-review",
+      "prompt": "What is the value of \\(\\dfrac{5^{7}}{5^{4}}\\)?",
+      "explanation": "Same base, division — **subtract** the exponents:\n\n\\[\\frac{5^{7}}{5^{4}} = 5^{7-4} = 5^{3} = 125\\]\n\nThe answer is **125**.\n\n**The traps:** choice **E** (\\(5^{11}\\)) *adds* the exponents, which is the rule for\n*multiplication*, not division. Choices that divide the exponents (\\(7 \\div 4\\)) or cancel bases\nincorrectly land on the smaller powers of 5.",
+      "hints": [
+        "Same base with division: what do you do to the exponents?",
+        "\\(5^{7} / 5^{4} = 5^{7-4}\\). Now just evaluate the small power."
+      ]
+    },
+    {
+      "id": "quant-arithmetic-exponents-roots-0018",
+      "section": "quant",
+      "topic": "arithmetic",
+      "subtopic": "exponents-roots",
+      "type": "problem-solving",
+      "difficulty": "easy",
+      "tags": [
+        "exponents",
+        "zero-exponent",
+        "negative-exponent"
+      ],
+      "choices": {
+        "A": "0",
+        "B": "1",
+        "C": "1.25",
+        "D": "1.5",
+        "E": "9"
+      },
+      "answer": "C",
+      "author": "openmat",
+      "reviewers": [],
+      "status": "in-review",
+      "prompt": "What is the value of \\(7^{0} + 2^{-2}\\)?",
+      "explanation": "Handle each term with the definitions of the zero and negative exponents:\n\n\\[7^{0} = 1, \\qquad 2^{-2} = \\frac{1}{2^{2}} = \\frac{1}{4}\\]\n\nSo the sum is\n\n\\[1 + \\frac{1}{4} = \\frac{5}{4} = 1.25\\]\n\nThe answer is **1.25**.\n\n**The traps:** choice **A (0)** assumes \\(7^0 = 0\\), but any nonzero base to the zero power is 1.\nChoice **E (9)** reads \\(2^{-2}\\) as \\(-2\\times 2\\) or \\(2^2\\) plus a sign slip — a negative exponent\ngives a positive *reciprocal*, not a negative number.",
+      "hints": [
+        "Any nonzero number raised to the power 0 equals 1 — not 0.",
+        "A negative exponent means take the reciprocal: \\(2^{-2} = 1/2^{2}\\), a positive fraction."
+      ]
+    },
+    {
+      "id": "quant-arithmetic-exponents-roots-0019",
+      "section": "quant",
+      "topic": "arithmetic",
+      "subtopic": "exponents-roots",
+      "type": "problem-solving",
+      "difficulty": "medium",
+      "tags": [
+        "exponents",
+        "power-of-a-power",
+        "product-rule",
+        "variables"
+      ],
+      "choices": {
+        "A": "x^{9}",
+        "B": "x^{10}",
+        "C": "x^{12}",
+        "D": "x^{14}",
+        "E": "x^{24}"
+      },
+      "answer": "B",
+      "author": "openmat",
+      "reviewers": [],
+      "status": "in-review",
+      "prompt": "For \\(x \\neq 0\\), which of the following is equal to \\(\\left(x^{2}\\right)^{3} \\cdot x^{4}\\)?",
+      "explanation": "Apply the rules in order. First, **power of a power** — multiply the exponents:\n\n\\[\\left(x^{2}\\right)^{3} = x^{2\\cdot 3} = x^{6}\\]\n\nThen the **product rule** — same base, add the exponents:\n\n\\[x^{6} \\cdot x^{4} = x^{6+4} = x^{10}\\]\n\nThe answer is **\\(x^{10}\\)**.\n\n**The traps:** choice **E** (\\(x^{24}\\)) multiplies all three exponents (\\(2\\cdot 3\\cdot 4\\)) as if\neverything were a power of a power. Choice **A** (\\(x^{9}\\)) adds \\(2+3+4\\), mixing up which\noperation adds and which multiplies. Multiply for a power raised to a power; add when multiplying\nlike bases.",
+      "hints": [
+        "Do the inner operation first: \\((x^2)^3\\) is a power raised to a power.",
+        "Once you have a single power of \\(x\\) times another, add those two exponents."
+      ]
+    },
+    {
+      "id": "quant-arithmetic-exponents-roots-0020",
+      "section": "quant",
+      "topic": "arithmetic",
+      "subtopic": "exponents-roots",
+      "type": "problem-solving",
+      "difficulty": "medium",
+      "tags": [
+        "roots",
+        "radicals",
+        "simplifying-radicals"
+      ],
+      "choices": {
+        "A": "\\\\sqrt{68}",
+        "B": "2\\\\sqrt{17}",
+        "C": "8\\\\sqrt{2}",
+        "D": "15\\\\sqrt{2}",
+        "E": "34"
+      },
+      "answer": "C",
+      "author": "openmat",
+      "reviewers": [],
+      "status": "in-review",
+      "prompt": "What is \\(\\sqrt{50} + \\sqrt{18}\\) in simplest form?",
+      "explanation": "Pull the perfect-square factor out of each radical, then combine the *like* radicals:\n\n\\[\\sqrt{50} = \\sqrt{25 \\cdot 2} = 5\\sqrt{2}, \\qquad \\sqrt{18} = \\sqrt{9 \\cdot 2} = 3\\sqrt{2}\\]\n\nBoth are multiples of \\(\\sqrt2\\), so add the coefficients:\n\n\\[5\\sqrt{2} + 3\\sqrt{2} = 8\\sqrt{2}\\]\n\nThe answer is **\\(8\\sqrt{2}\\)**.\n\n**The traps:** choice **A** (\\(\\sqrt{68}\\)) adds *under* the radical (\\(50+18\\)), but\n\\(\\sqrt{a} + \\sqrt{b} \\neq \\sqrt{a+b}\\). Choice **D** (\\(15\\sqrt2\\)) multiplies the coefficients\ninstead of adding them. You may add radicals only when the parts under the root already match.",
+      "hints": [
+        "Factor out the largest perfect square from each radical first.",
+        "After simplifying, both terms are multiples of \\(\\sqrt2\\). Add only the numbers in front."
+      ]
+    },
+    {
+      "id": "quant-arithmetic-exponents-roots-0021",
+      "section": "quant",
+      "topic": "arithmetic",
+      "subtopic": "exponents-roots",
+      "type": "problem-solving",
+      "difficulty": "medium",
+      "tags": [
+        "exponents",
+        "fractional-exponents",
+        "roots"
+      ],
+      "choices": {
+        "A": "6",
+        "B": "9",
+        "C": "18",
+        "D": "81",
+        "E": "729"
+      },
+      "answer": "B",
+      "author": "openmat",
+      "reviewers": [],
+      "status": "in-review",
+      "prompt": "What is the value of \\(27^{2/3}\\)?",
+      "explanation": "A fractional exponent combines a root and a power: the denominator is the root, the numerator is the\npower. Take the root **first** to keep the numbers small:\n\n\\[27^{2/3} = \\left(27^{1/3}\\right)^{2} = \\left(\\sqrt[3]{27}\\right)^{2} = 3^{2} = 9\\]\n\nThe answer is **9**.\n\n**The traps:** choice **E** (\\(729 = 27^2\\)) ignores the cube root entirely. Choice **C (18)**\nmultiplies the base by the exponent (\\(27 \\times \\tfrac23\\)). Choice **A (6)** takes the cube root\nbut then multiplies by 2 instead of squaring.",
+      "hints": [
+        "Rewrite the exponent as a root and a power: the bottom of the fraction is the root.",
+        "Cube root of 27 is a small number — find it first, then apply the remaining power."
+      ]
+    },
+    {
+      "id": "quant-arithmetic-exponents-roots-0022",
+      "section": "quant",
+      "topic": "arithmetic",
+      "subtopic": "exponents-roots",
+      "type": "problem-solving",
+      "difficulty": "hard",
+      "tags": [
+        "exponents",
+        "exponential-equations",
+        "same-base"
+      ],
+      "choices": {
+        "A": "2",
+        "B": "3",
+        "C": "4",
+        "D": "5",
+        "E": "7"
+      },
+      "answer": "D",
+      "author": "openmat",
+      "reviewers": [],
+      "status": "in-review",
+      "prompt": "If \\(4^{x+1} = 8^{x-1}\\), what is the value of \\(x\\)?",
+      "explanation": "The bases 4 and 8 are both powers of 2, so rewrite everything with base 2:\n\n\\[4^{x+1} = \\left(2^{2}\\right)^{x+1} = 2^{2(x+1)}, \\qquad 8^{x-1} = \\left(2^{3}\\right)^{x-1} = 2^{3(x-1)}\\]\n\nWith a common base, the exponents must be equal:\n\n\\[2(x+1) = 3(x-1)\\]\n\\[2x + 2 = 3x - 3\\]\n\\[x = 5\\]\n\nThe answer is **5**.\n\n**Check:** \\(4^{6} = 4096\\) and \\(8^{4} = 4096\\). ✓\n\n**The trap:** trying to compare 4 and 8 directly, or guessing a small value, misses the key move —\nexpress both sides as powers of the same prime, then set the exponents equal.",
+      "hints": [
+        "Both 4 and 8 are powers of 2. Rewrite each side with base 2.",
+        "Once the bases match, the exponents must be equal — solve the resulting linear equation."
+      ]
+    },
     {
       "id": "quant-arithmetic-fractions-decimals-0015",
       "section": "quant",
@@ -968,6 +1148,23 @@
       "status": "in-review",
       "body": "## Overview\n\nA quadratic equation has the form \\(ax^2 + bx + c = 0\\). On GMAT Focus Quant, most quadratics are\nbuilt to **factor cleanly**, so factoring — not the quadratic formula — is usually the fast route.\n\n## Core concepts\n\n**Factoring \\(x^2 + bx + c\\).** Find two numbers that **multiply to \\(c\\)** and **add to \\(b\\)**.\nThen \\(x^2 + bx + c = (x + p)(x + q)\\), and the solutions make each factor zero.\n\nExample: \\(x^2 - 5x + 6\\). Two numbers multiplying to \\(+6\\) and adding to \\(-5\\) are \\(-2\\) and\n\\(-3\\), so \\((x-2)(x-3) = 0\\) and \\(x = 2\\) or \\(x = 3\\).\n\n**Sum and product shortcut.** For \\(x^2 + bx + c = 0\\):\n\n\\[\\text{sum of roots} = -b, \\qquad \\text{product of roots} = c\\]\n\nThis lets you answer \"sum/product of solutions\" questions without fully solving.\n\n**Special products** worth recognizing instantly:\n\n\\[a^2 - b^2 = (a-b)(a+b), \\quad (a+b)^2 = a^2 + 2ab + b^2, \\quad (a-b)^2 = a^2 - 2ab + b^2\\]\n\n**The quadratic formula** (fallback when factoring is ugly):\n\n\\[x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}\\]\n\n## Worked examples\n\n**Factor and solve.** \\(x^2 + 2x - 15 = 0 \\Rightarrow (x+5)(x-3) = 0 \\Rightarrow x = -5 \\text{ or } 3\\).\n\n**Difference of squares.** \\(x^2 - 49 = 0 \\Rightarrow (x-7)(x+7) = 0 \\Rightarrow x = \\pm 7\\).\n\n## Common traps\n\n- **Confusing sum and product of roots.** Sum is \\(-b\\), product is \\(c\\). Read which the question wants.\n- **Dropping a solution.** A quadratic usually has *two* roots — check whether the question wants both, their sum, or only positive values.\n- **Sign errors in factoring.** Verify by expanding your factors back out.\n\n## Key takeaways\n\n- Factor into \\((x + p)(x + q)\\) where \\(pq = c\\) and \\(p + q = b\\); each factor set to zero gives a root.\n- Sum of roots \\(= -b\\), product \\(= c\\) — a fast shortcut.\n- Recognize the difference of squares and perfect-square forms on sight."
     },
+    {
+      "id": "quant-arithmetic-exponents-roots",
+      "section": "quant",
+      "topic": "arithmetic",
+      "subtopic": "exponents-roots",
+      "title": "Exponents & Roots",
+      "tags": [
+        "exponents",
+        "roots",
+        "radicals",
+        "powers"
+      ],
+      "author": "openmat",
+      "reviewers": [],
+      "status": "in-review",
+      "body": "## Overview\n\nExponents and roots show up all over GMAT Focus Quant — inside number-properties questions, in\ndisguised equations, and as the fast way to compare very large or very small quantities. Almost\neverything reduces to a short list of rules plus one habit: **rewrite every base as a power of the\nsame prime before you do anything else.**\n\n## Core concepts\n\n**The exponent rules.** For any nonzero base and integer (or rational) exponents:\n\n- Product: \\(a^m \\cdot a^n = a^{m+n}\\) — same base, *add* exponents.\n- Quotient: \\(\\dfrac{a^m}{a^n} = a^{m-n}\\) — same base, *subtract* exponents.\n- Power of a power: \\((a^m)^n = a^{mn}\\) — *multiply* exponents.\n- Distributes over products: \\((ab)^n = a^n b^n\\).\n\n**Zero and negative exponents.**\n\n\\[a^0 = 1 \\quad (a \\ne 0), \\qquad a^{-n} = \\frac{1}{a^n}\\]\n\nA negative exponent means \"reciprocal,\" not \"negative number.\" So \\(2^{-2} = \\tfrac14\\), which is\npositive.\n\n**Roots are fractional exponents.** This is the single most useful bridge:\n\n\\[\\sqrt[n]{a} = a^{1/n}, \\qquad a^{m/n} = \\left(\\sqrt[n]{a}\\right)^m = \\sqrt[n]{a^m}\\]\n\nSo \\(27^{2/3} = \\left(27^{1/3}\\right)^2 = 3^2 = 9\\). Take the root first (smaller numbers), then the power.\n\n**Simplifying radicals.** Pull perfect-square factors out from under a square root, and combine only\n*like* radicals:\n\n\\[\\sqrt{ab} = \\sqrt{a}\\,\\sqrt{b}, \\qquad \\sqrt{50} = \\sqrt{25\\cdot 2} = 5\\sqrt{2}\\]\n\nYou can add \\(5\\sqrt2 + 3\\sqrt2 = 8\\sqrt2\\), but you **cannot** turn \\(\\sqrt2 + \\sqrt2\\) into\n\\(\\sqrt4\\).\n\n**Same-base strategy for equations.** When an equation has different bases that are all powers of one\nprime, rewrite them and set the exponents equal:\n\n\\[4^{x+1} = 8^{x-1} \\;\\Rightarrow\\; 2^{2(x+1)} = 2^{3(x-1)} \\;\\Rightarrow\\; 2x+2 = 3x-3 \\;\\Rightarrow\\; x = 5\\]\n\n## Worked examples\n\n**Combine rules.** Simplify \\((x^2)^3 \\cdot x^4\\). Power of a power gives \\(x^{6}\\); then the product\nrule adds exponents: \\(x^{6} \\cdot x^{4} = x^{10}\\).\n\n**Fractional exponent.** Evaluate \\(27^{2/3}\\). Cube root of 27 is 3; square it: \\(3^2 = 9\\).\n\n**Radicals.** Simplify \\(\\sqrt{50} + \\sqrt{18} = 5\\sqrt2 + 3\\sqrt2 = 8\\sqrt2\\).\n\n## Common traps\n\n- **Multiplying exponents when you should add.** \\(2^5 \\cdot 2^3 = 2^{8}\\), not \\(2^{15}\\). You only\n  multiply exponents for a *power of a power*, \\((2^5)^3 = 2^{15}\\).\n- **Negative exponent → negative number.** \\(3^{-1} = \\tfrac13\\), a positive fraction, not \\(-3\\).\n- **Adding under the radical.** \\(\\sqrt{a} + \\sqrt{b} \\ne \\sqrt{a+b}\\). \\(\\sqrt{9} + \\sqrt{16} = 3+4 = 7\\), not \\(\\sqrt{25} = 5\\).\n- **Combining unlike bases.** \\(2^3 \\cdot 3^3\\) is \\((2\\cdot3)^3 = 6^3\\), but \\(2^3 \\cdot 3^2\\) cannot be merged into one base.\n\n## Key takeaways\n\n- Same base: add exponents to multiply, subtract to divide, multiply to raise a power to a power.\n- \\(a^0 = 1\\) and \\(a^{-n} = 1/a^n\\); negative exponents give positive reciprocals.\n- Roots are fractional exponents: \\(a^{m/n} = \\sqrt[n]{a^m}\\) — take the root first, then the power.\n- To solve exponential equations, rewrite every base as the same prime and equate the exponents."
+    },
     {
       "id": "quant-arithmetic-percents-ratios",
       "section": "quant",
diff --git a/growth/LOG.md b/growth/LOG.md
new file mode 100644
index 0000000..5427794
--- /dev/null
+++ b/growth/LOG.md
@@ -0,0 +1,29 @@
+# Growth Log
+
+Running record of what each growth run produced, so runs don't repeat work. Newest first.
+See [`STRATEGY.md`](./STRATEGY.md) for the playbook. **"Needs human"** = an action only the
+account owner can take (publishing an external post, a decision).
+
+---
+
+## 2026-07-21 — Bootstrap: playbook + launch drafts + contributor issues
+
+- **Added the growth playbook** (`STRATEGY.md`): ICP, messaging pillars, channels, the daily-run
+  operating procedure, metrics, guardrails, and a backlog. This is now the canonical growth guide.
+- **Drafted the r/GMAT launch post** → [`posts/2026-07-21-reddit-r-gmat-launch.md`](./posts/2026-07-21-reddit-r-gmat-launch.md).
+  **Needs human:** review + post to r/GMAT (check subreddit self-promo rules first; flair if required).
+- **Drafted the Show HN post** → [`posts/2026-07-21-show-hn.md`](./posts/2026-07-21-show-hn.md).
+  **Needs human:** hold until the question bank is deeper (aim ~75–100+ verified), then post from the owner's HN account. One good shot — don't waste it early.
+- **Created contributor-onboarding GitHub issues** (`good first issue` / `help wanted`) — see the
+  issues tab. **Needs human:** add the `good first issue` and `help wanted` labels in repo settings
+  if they don't exist yet, and consider pinning the "Start here" issue.
+- **Baseline (2026-07-21):** stars/forks/external contributors ≈ 0; 38 questions, 9 lessons in the
+  bank; no site analytics yet. First targets: first non-founder star, first external PR, first
+  user feedback issue.
+
+### Queued for upcoming runs (from the backlog)
+- Set repo topics/description; pin a "Start here" issue.
+- Product issue: add privacy-respecting analytics so traffic is measurable.
+- Draft GMAT Club forum intro post.
+- In-site one-click "report a bad answer" feedback link.
+- Awesome-list target list + submission PRs.
diff --git a/growth/STRATEGY.md b/growth/STRATEGY.md
new file mode 100644
index 0000000..17c786f
--- /dev/null
+++ b/growth/STRATEGY.md
@@ -0,0 +1,102 @@
+# OpenMat Growth Playbook
+
+> **This is the canonical growth strategy for OpenMat, and the operating manual for the daily
+> growth run.** It plays the same role for user/contributor acquisition that
+> [`curriculum.md`](../curriculum.md) plays for content: every growth run consults this file,
+> executes the next highest-value item, logs it in [`LOG.md`](./LOG.md), and stops.
+>
+> It is intentionally public. OpenMat is an open project; building in the open is on-brand and
+> costs nothing.
+
+## The goal
+
+Three outcomes, in priority order:
+
+1. **Users** — GMAT Focus test-takers who study on the site and come back.
+2. **Contributors** — people who write/review questions and lessons, or improve the code.
+3. **Feedback** — a tight loop so the product improves faster than we guess.
+
+Users and contributors reinforce each other: a bigger question bank attracts more studiers, and
+more studiers surface more contributors and better feedback. The strategy optimizes that flywheel.
+
+## Who we're talking to (ICP)
+
+| Audience | Where they are | What they want | Our hook |
+|----------|----------------|----------------|----------|
+| **Cost-sensitive test-takers** | r/GMAT, GMAT Club forums, GMAT Discord servers, YouTube comments | Free, current (Focus Edition) practice with real explanations | "Free forever, open-source. No paywall, no trial." |
+| **High scorers / tutors** | r/GMAT, LinkedIn, GMAT Club | To give back, build a public teaching portfolio, signal expertise | "Your name on verified questions thousands study from." |
+| **OSS / edtech developers** | Hacker News, Lobsters, dev.to, GitHub | Meaningful side projects, clean codebases to contribute to | "Plain Markdown + JSON, no DB, good-first-issues, MIT/CC-BY-SA." |
+| **MBA applicants (broad)** | LinkedIn, r/MBA, Twitter/X | Anything that lowers the cost of applying | "The community-built GMAT prep." |
+
+## Messaging pillars (use these consistently)
+
+1. **Free forever, genuinely open** — CC-BY-SA content, MIT code. A real alternative to $150–350 courses.
+2. **Built for the current exam** — GMAT **Focus Edition**, not the retired classic format (this is a real differentiator; a lot of free material online is stale).
+3. **Quality-controlled, original** — `draft → in-review → verified`; no copied GMAC content; a wrong answer is worse than no question.
+4. **Yours to build on** — fork it, translate it, remix it. Contributors get real credit.
+
+Always link the study site (<https://dmdaudio.github.io/OpenMat/>) for users and the repo for contributors.
+
+## Channels & tactics
+
+**Owned / compounding (do these first — they work while we sleep):**
+- **GitHub discoverability** — repo topics/tags, a crisp description, `good first issue` + `help wanted` labels, a pinned "start here" issue, badges. Gets us found by developers and shows up in GitHub search.
+- **SEO-friendly content** — the study site itself; lesson pages are indexable, evergreen search bait for "free GMAT Focus [topic] practice."
+- **"Awesome list" inclusion** — PRs adding OpenMat to relevant awesome-* and free-resources lists (respect each list's criteria).
+
+**Community (highest user intent — respect each community's self-promo rules):**
+- **r/GMAT** — by far the highest-intent audience. Lead with value (a free resource + a genuine ask for feedback), never a naked ad. Read the subreddit rules each time; many require flairing self-promo and limit frequency.
+- **GMAT Club forums** — long-lived threads, strong SEO. A "free open-source question bank" thread.
+- **GMAT Discord / study servers** — share in resource channels, offer to take feedback.
+
+**Developer / launch (bursty — good for contributors & a traffic spike):**
+- **Show HN** — the OSS + edtech angle. One good shot; time it when the bank is meaty enough to impress.
+- **Lobsters / dev.to / Hashnode** — write-up of how it's built (Markdown-as-database, zero-dependency build).
+- **Product Hunt** — later, once the site is polished and the bank is deep.
+
+**Direct (relationship-building):**
+- **LinkedIn / X** — short build-in-public updates ("this week OpenMat added X verified questions"). Compounds slowly, reaches applicants + tutors.
+
+## The daily growth run: operating procedure
+
+Each run does **one** unit of high-value work, end to end, and stops. Don't try to do everything.
+
+1. **Read [`LOG.md`](./LOG.md)** to see what's already done and what's queued. Never repeat a post or re-file a duplicate issue.
+2. **Pick the next item** — highest value not yet done. Rough weekly rotation to stay balanced:
+   - *Owned/compounding* (discoverability, README, labels, awesome-lists) — bias here early; it compounds.
+   - *A ready-to-publish post draft* for one channel (save under [`posts/`](./posts/), dated).
+   - *Contributor onboarding* — create/curate 1–3 well-scoped `good first issue`s.
+   - *Feedback synthesis* — read new issues/PRs/comments, distill into a short "what users are telling us" note and, if warranted, product issues.
+3. **Produce the artifact** — a committed file (post draft, doc, label/README change) and/or an in-scope GitHub issue. Keep external *posting* for a human unless explicitly authorized (see guardrails).
+4. **Log it** in `LOG.md` (date, what, where it lives, what a human still needs to do).
+5. **Open/att­ach to the PR** for committed changes; **notify** the user with anything that needs them (posts to publish, decisions).
+
+## Metrics to watch (report movement, not vanity)
+
+- GitHub **stars, forks, unique contributors**, external issues/PRs opened.
+- Study-site **traffic** (if/when analytics are added — see backlog).
+- Community **engagement** (Reddit upvotes/comments, HN points, Discord reactions) on things we posted.
+- **Content depth** (questions/lessons, % verified) — the product metric that makes all the above easier.
+
+Baseline is roughly zero today; the first job is to establish the baseline and get the first non-founder star, user, and contributor.
+
+## Guardrails (non-negotiable)
+
+- **A human publishes external posts.** Drafts are prepared here; the account owner reviews and posts. Never assume prior approval carries to a new post.
+- **No spam, no astroturfing.** One genuine post per community, following its rules. Never fabricate reviews, testimonials, upvotes, or sockpuppet accounts.
+- **Be transparent.** Don't hide that the project is early or that content is community/AI-assisted where a community's norms expect disclosure.
+- **No impersonation** of GMAC, tutors, or any person/org. OpenMat is unaffiliated with GMAC — say so where relevant.
+- **Respect copyright.** Never reproduce real GMAT questions or paid-course material anywhere, including promo.
+- **GitHub actions stay in scope** (`dmdaudio/openmat`) and proportionate — a few high-quality issues, not a flood.
+
+## Backlog (living — check LOG.md for status)
+
+- [ ] Set repo topics/description + `good first issue` / `help wanted` labels; pin a "Start here" issue.
+- [ ] Draft the r/GMAT launch post (value-first, feedback ask).
+- [ ] Draft the Show HN post (time it for when the bank is deeper).
+- [ ] Create 3–5 `good first issue`s (write one question in an uncovered subtopic; review an in-review question; small site UX fixes).
+- [ ] Add privacy-respecting, self-hosted-friendly analytics to the study site (so we can measure traffic) — as a product issue.
+- [ ] Draft a GMAT Club forum intro post.
+- [ ] Build a "free GMAT resources" awesome-list target list and submit PRs.
+- [ ] Add a lightweight in-site feedback link (GitHub issue template deep-link) so users can report bad answers in one click.
+- [ ] Build-in-public LinkedIn/X update template + weekly cadence.
diff --git a/growth/posts/2026-07-21-reddit-r-gmat-launch.md b/growth/posts/2026-07-21-reddit-r-gmat-launch.md
new file mode 100644
index 0000000..eb25184
--- /dev/null
+++ b/growth/posts/2026-07-21-reddit-r-gmat-launch.md
@@ -0,0 +1,46 @@
+---
+channel: Reddit — r/GMAT
+status: draft — needs human to post
+suggested_flair: Study Material / Resource (check current subreddit options)
+notes: >
+  Read r/GMAT's rules before posting — self-promo is often restricted and may need flair or a
+  set frequency. Post from a real account with some history, not a throwaway. Lead with value and
+  a genuine feedback ask, not a sell. Reply to every comment; treat it as a feedback session.
+---
+
+**Title:** I built a free, open-source GMAT Focus question bank + study site — would love your feedback (and questions you wish existed)
+
+**Body:**
+
+GMAT prep courses run $150–350, and a lot of the free stuff online is still written for the old
+classic format. So I started **OpenMat** — a free, open-source practice bank and study site built
+specifically for the **GMAT Focus Edition**.
+
+What's there right now:
+
+- A growing bank of **original** practice questions (Quant, Verbal, Data Insights) with full worked
+  explanations and hints — not just an answer key.
+- A study site with instant feedback, a per-question timer set to GMAT pacing, and a local profile
+  that tracks your progress in your browser (nothing to sign up for).
+- Everything tagged to a shared topic taxonomy, so you can drill a specific subtopic.
+
+A few honest things:
+
+- It's **early**. The bank is still small and growing — I'd rather say that than oversell it.
+- It's **free forever** and openly licensed. No paywall, no "premium tier," no email wall.
+- All content is **original** — no copied real GMAT questions (those are GMAC's). Every question
+  goes through a review step before it's marked verified, because a wrong answer is worse than none.
+- I'm **not affiliated with GMAC** in any way.
+
+Study site: https://dmdaudio.github.io/OpenMat/
+
+What I'd love from you:
+
+1. **Try a few questions and tell me where the explanations are weak or an answer looks wrong.**
+   That feedback is the single most useful thing right now.
+2. **What topics/subtopics do you most wish had more practice?** I'll prioritize those.
+3. If you scored well and want to **write or review** a few questions, the whole thing is
+   community-built and I'd genuinely welcome the help (there's a simple contribution guide).
+
+Not trying to replace your prep — just trying to make a solid free option exist for the current
+exam. Thanks, and good luck to everyone testing soon.
diff --git a/growth/posts/2026-07-21-show-hn.md b/growth/posts/2026-07-21-show-hn.md
new file mode 100644
index 0000000..18a1c9d
--- /dev/null
+++ b/growth/posts/2026-07-21-show-hn.md
@@ -0,0 +1,44 @@
+---
+channel: Hacker News — Show HN
+status: draft — HOLD until the bank is deeper (~75–100+ verified questions), then human posts
+notes: >
+  You get essentially one good Show HN. Time it when the site is impressive enough to convert the
+  traffic spike into stars/contributors. Post in the morning US Eastern on a weekday. The HN
+  audience skews developer, so the angle is the open, hackable architecture + the free-education
+  mission — not GMAT tips. Be present in the comments for the first few hours; answer technical
+  questions directly and honestly about how early it is.
+---
+
+**Title:** Show HN: OpenMat – Open-source, community-built GMAT Focus prep (free forever)
+
+**URL:** https://github.com/DMDaudio/OpenMat
+
+**Body (first comment):**
+
+Hi HN. OpenMat is a free, open-source practice bank and study site for the GMAT Focus Edition (the
+current exam). Commercial prep courses cost $150–350, so I wanted a genuinely free, openly-licensed
+alternative that anyone can study from, fork, translate, or build on.
+
+Architecture, since this crowd will care:
+
+- **Content is the database.** Every question and lesson is a single Markdown file with a YAML
+  front-matter block, validated against JSON Schema. No DB, no CMS. This makes every contribution a
+  readable pull-request diff and keeps quality review human-friendly.
+- **Zero-dependency build.** A ~200-line Node script scans the content tree and emits one
+  `content.json` the static site consumes. Deterministic output so CI stays quiet. The site is
+  plain HTML/CSS/JS on GitHub Pages — KaTeX for math, a local-first profile in `localStorage` with
+  export/import, and optional Supabase sync that's off by default (no server to run).
+- **Quality workflow.** Content moves `draft → in-review → verified`; nothing ships as verified
+  until a second person checks the answer and explanation. All content is original — no copied GMAC
+  questions.
+- **Licensing:** content CC-BY-SA-4.0, code MIT.
+
+It's early and the question bank is still growing — I'm posting partly to find contributors
+(there are good-first-issues) and partly for feedback on the approach of treating a
+prep-content library as a reviewable, forkable Git repo instead of a walled garden.
+
+Study site: https://dmdaudio.github.io/OpenMat/
+Repo: https://github.com/DMDaudio/OpenMat
+
+Not affiliated with GMAC. Happy to answer anything about the content pipeline or the local-first
+data model.