Formula
aⁿ = a × a × … × a (n times)a⁻ⁿ = 1 ÷ aⁿa^(1/n) = ⁿ√a, a^(m/n) = (ⁿ√a)ᵐa⁰ = 1 (a ≠ 0) How it works
An exponent tells you how many times to multiply the base by itself: 2¹⁰ means ten 2s multiplied together, which is 1024. Exponents are shorthand for repeated multiplication, just as multiplication is shorthand for repeated addition.
Negative exponents flip the number into a fraction, so 2⁻³ = 1/8 = 0.125. Fractional exponents are roots: 9^0.5 is the square root of 9, and 8^(1/3) is the cube root of 8.
The key rules: when you multiply powers with the same base, add the exponents (aᵐ·aⁿ = aᵐ⁺ⁿ); when you divide, subtract them; and a power of a power multiplies them ((aᵐ)ⁿ = aᵐⁿ).
Frequently asked questions
Why is anything to the power 0 equal to 1?
Follow the pattern: 2³ = 8, 2² = 4, 2¹ = 2 — each step divides by 2. One more step gives 2⁰ = 1. It also keeps the rule aᵐ ÷ aᵐ = aᵐ⁻ᵐ = a⁰ = 1 consistent.
Is −2² equal to 4 or −4?
By convention −2² = −(2²) = −4, because exponents are applied before the minus sign. To square negative two, write (−2)² = 4. Here, entering −2 as the base squares the whole −2.