Exponent Rules — Laws of Exponents Reference
aⁿ × aᵐ = aⁿ⁺ᵐProduct Rule
Same base: add exponents
Example: 2³ × 2⁴ = 2⁷ = 128
aⁿ ÷ aᵐ = aⁿ⁻ᵐQuotient Rule
Same base: subtract exponents
Example: 3⁵ ÷ 3² = 3³ = 27
(aⁿ)ᵐ = aⁿˣᵐPower of a Power
Multiply exponents
Example: (2³)² = 2⁶ = 64
(ab)ⁿ = aⁿ × bⁿPower of a Product
Distribute exponent
Example: (2×3)² = 2²×3² = 36
(a/b)ⁿ = aⁿ/bⁿPower of a Quotient
Distribute exponent
Example: (4/2)³ = 4³/2³ = 8
a⁰ = 1Zero Exponent
Any base (≠0) raised to 0 = 1
Example: 5⁰ = 1, 100⁰ = 1
a⁻ⁿ = 1/aⁿNegative Exponent
Reciprocal of base
Example: 2⁻³ = 1/2³ = 1/8
a^(1/n) = ⁿ√aFractional Exponent
Fractional exponent = root
Example: 8^(1/3) = ³√8 = 2
a^(m/n) = ⁿ√(aᵐ)General Fractional Exp.
Root of the power
Example: 4^(3/2) = √(4³) = 8
a¹ = aExponent One
Any number to the power of 1 = itself
Example: 7¹ = 7
Common Powers Table
| n | n² | n³ | n⁴ | n⁵ | n¹⁰ |
|---|---|---|---|---|---|
| 2 | 4 | 8 | 16 | 32 | 1,024 |
| 3 | 9 | 27 | 81 | 243 | 59,049 |
| 4 | 16 | 64 | 256 | 1,024 | 1,048,576 |
| 5 | 25 | 125 | 625 | 3,125 | 9,765,625 |
| 6 | 36 | 216 | 1,296 | 7,776 | 60,466,176 |
| 7 | 49 | 343 | 2,401 | 16,807 | 282,475,249 |
| 8 | 64 | 512 | 4,096 | 32,768 | 1,073,741,824 |
| 9 | 81 | 729 | 6,561 | 59,049 | 3,486,784,401 |
| 10 | 100 | 1000 | 10,000 | 100,000 | 10,000,000,000 |