Exponents & Radicals
Exponents tell you how many times to multiply a base by itself. Radicals are the inverse — finding what number was repeatedly multiplied.
Exponent Rules
| Rule | Formula | Example |
|---|---|---|
| Product | aᵐ × aⁿ = aᵐ⁺ⁿ | x³ × x² = x⁵ |
| Quotient | aᵐ ÷ aⁿ = aᵐ⁻ⁿ | x⁵ ÷ x² = x³ |
| Power | (aᵐ)ⁿ = aᵐⁿ | (x²)³ = x⁶ |
| Zero | a⁰ = 1 | 7⁰ = 1 |
| Negative | a⁻ⁿ = 1/aⁿ | x⁻² = 1/x² |
Radicals
√n means "what squared gives n?" Cube root ∛n means "what cubed gives n?"
√49 = 7 | ∛27 = 3 | √72 = √(36×2) = 6√2
Rational Exponents
a^(m/n) = (ⁿ√a)ᵐ
8^(2/3) = (∛8)² = 2² = 4
25^(1/2) = √25 = 5
Simplifying Radical Expressions
Factor out perfect squares (or cubes). Combine like radicals just like like terms.
3√2 + 5√2 = 8√2 | √50 = 5√2
FAQ
Can you add √2 + √3? No — they are unlike radicals. Leave as is.
What is (−2)⁴? 16 — even exponent makes it positive.
Quick Quiz
Test what you just learned. Choose the best answer for each question.