Module · Arithmetic & Number Properties
Chapter 9: Exponents & Roots
Arithmetic
5 topics
What this chapter covers
The 5 topics below make up Exponents & Roots on the GRE. Click any topic to open its notes, examples and practice test.
1Laws of Exponents
2Negative & Fractional Exponents
3Square & Cube Roots
4Simplifying Radicals
5Scientific Notation
Study material & tests
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Notes, worked examples and hint-guided practice for every topic.
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🎯 Topic tests
8 auto-graded questions per topic, pulled from the question bank.
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📝 Chapter test
25 fresh mixed-difficulty questions, timed, with full solutions.
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Formula Reference Sheet
This chapter
Laws of exponents
| Product | aᵐ · aⁿ = aᵐ⁺ⁿ |
|---|---|
| Quotient | aᵐ / aⁿ = aᵐ⁻ⁿ |
| Power of a power | (aᵐ)ⁿ = aᵐⁿ |
| Power of a product | (ab)ⁿ = aⁿ bⁿ |
| Zero & negative | a⁰ = 1 (a ≠ 0); a⁻ⁿ = 1/aⁿ |
Roots & radicals
| Fractional exponent | a^(m/n) = ⁿ√(aᵐ) = (ⁿ√a)ᵐ |
|---|---|
| Product / quotient of roots | √a · √b = √(ab); √a / √b = √(a/b) |
| Simplify a radical | √(k²·m) = k√m (pull out perfect squares) |
| Scientific notation | a × 10ⁿ with 1 ≤ a < 10 |
GRE reference
🖩 Graphing Calculator