Exponent Rules & Powers

REF

Exponent Laws

Rule Name Rule Example
Product Rule aᵐ × aⁿ = aᵐ⁺ⁿ 2³ × 2² = 2⁵ = 32
Quotient Rule aᵐ ÷ aⁿ = aᵐ⁻ⁿ 3⁵ ÷ 3² = 3³ = 27
Power Rule (aᵐ)ⁿ = aᵐⁿ (2³)² = 2⁶ = 64
Power of Product (ab)ⁿ = aⁿbⁿ (2×3)² = 2²×3² = 36
Power of Quotient (a/b)ⁿ = aⁿ/bⁿ (4/2)³ = 4³/2³ = 8
Zero Exponent a⁰ = 1 5⁰ = 1
Negative Exponent a⁻ⁿ = 1/aⁿ 2⁻³ = 1/2³ = 1/8
Fractional Exponent a¹/ⁿ = ⁿ√a 16¹/² = √16 = 4

Powers of 2

Power Value Power Value Power Value
2⁰12⁵322¹⁰1,024
22⁶642¹¹2,048
42⁷1282¹²4,096
82⁸2562¹⁵32,768
2⁴162⁹5122²⁰1,048,576

Powers of 10

Power Value Name
10⁰1One
10¹10Ten
10²100Hundred
10³1,000Thousand
10⁶1,000,000Million
10⁹1,000,000,000Billion
10¹²1,000,000,000,000Trillion
10⁻¹0.1Tenth
10⁻²0.01Hundredth
10⁻³0.001Thousandth

Common Powers Table

Base ² ³
2481632
392781243
416642561,024
5251256253,125
6362161,2967,776
7493432,40116,807
8645124,09632,768
9817296,56159,049
101001,00010,000100,000

Understanding Exponents

An exponent indicates how many times a base number is multiplied by itself. For example, 2³ = 2×2×2 = 8. Exponents follow specific laws that simplify calculations: when multiplying same bases, add exponents; when dividing, subtract exponents. Zero exponent always equals 1. Negative exponents represent reciprocals. Exponents are fundamental in algebra, science, and computer science (especially powers of 2 in computing).