Exponents and radicals

Exponent rules let you simplify without computing: multiply means add exponents, divide means subtract, a power of a power means multiply. A square root is the exponent ½.

1. Write every number with the same base when you can (8 = 2³, 9 = 3²).
2. Apply the rules: aᵐ · aⁿ = aᵐ⁺ⁿ, aᵐ ÷ aⁿ = aᵐ⁻ⁿ, (aᵐ)ⁿ = aᵐⁿ, a⁰ = 1, a⁻ⁿ = 1/aⁿ.
3. Simplify roots by pulling out perfect squares: √50 = √25 · √2 = 5√2.

• Adding exponents when the bases are different: 2³ · 3² is not 6⁵.
• √(a + b) is not √a + √b. √(9 + 16) = 5, not 7.

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