MathAdvanced MathHigh frequency
SAT Math: Exponent Rules
37+ practice questions in Praczo
What you need to know
The concept, explained
- 1
Product rule: aᵐ × aⁿ = aᵐ⁺ⁿ — multiplying same-base terms, add the exponents.
- 2
Quotient rule: aᵐ / aⁿ = aᵐ⁻ⁿ — dividing same-base terms, subtract the exponents.
- 3
Power rule: (aᵐ)ⁿ = aᵐⁿ — raising a power to a power, multiply the exponents.
- 4
Negative exponents: a⁻ⁿ = 1/aⁿ. Fractional exponents: a^(m/n) = ⁿ√(aᵐ) — denominator is the root, numerator is the power.
- 5
Zero exponent: any nonzero base raised to 0 equals 1: a⁰ = 1.
Common mistakes
- ✗ Multiplying bases instead of adding exponents: x² × x³ = x⁵, not x⁶. The base stays the same.
- ✗ Applying the power rule to a sum: (x + y)² ≠ x² + y². You must expand with FOIL.
Try a sample question
SAT-style practice
Which expression is equivalent to (x³)² / x⁴?
37+ questions ready to practice
Ready to master this concept?
Praczo tracks your mastery on all 179 SAT concepts — not just broad topics. One sample question is a start; drilling to mastery is how scores move.
3-day free trial — no credit card required