Exponents, Roots & Order of Operations

aⁿ means a multiplied by itself n times (for positive integer n). Exponent laws let you rewrite products and quotients of powers with the same base without expanding everything.

Powers as repeated multiplication

aⁿ means a multiplied by itself n times (for positive integer n). Exponent laws let you rewrite products and quotients of powers with the same base without expanding everything.

Square roots and cube roots

√a is the non-negative number whose square is a. ∛a is the number whose cube is a (can be negative). Roots undo powers — carefully with domain and sign.

√(ab) = √a · √b for a,b ≥ 0.
√(a/b) = √a / √b for a ≥ 0, b > 0.
√(a²) = |a| — always take the absolute value for the principal square root.
Simplify radicals by factoring out perfect squares: √72 = √(36·2) = 6√2.