Learn it
- Product rule: aᵐ × aⁿ = aᵐ⁺ⁿ. 2³ × 2⁴ = 2⁷.
- Quotient rule: aᵐ ÷ aⁿ = aᵐ⁻ⁿ. 5⁶ ÷ 5² = 5⁴.
- Power rule: (aᵐ)ⁿ = aᵐⁿ. (3²)³ = 3⁶.
- Zero exponent: a⁰ = 1 (a ≠ 0).
- Negative exponent: a⁻ⁿ = 1/aⁿ. 2⁻³ = 1/8.
Worked examples
Example 1
Simplify 4² × 4³ and evaluate.
- Same base, add exponents: 4⁵
- 4⁵ = 1,024
Answer: 4⁵ = 1,024
Example 2
Simplify (x³)² ÷ x⁴.
- Power rule: x⁶
- Quotient rule: x⁶⁻⁴
Answer: x²
Practice
Try these on paper first, then check your work.
- 3² × 3⁵
- 10⁸ ÷ 10³
- (2³)²
- 5⁻²
Show the answer key
- 3⁷
- 10⁵
- 2⁶ = 64
- 1/25