An exponent (or power) tells you how many times to use a number in multiplication. In the expression a^n, "a" is the base and "n" is the exponent.
Key Rules
- a^m × a^n = a^(m+n)
- a^m / a^n = a^(m−n)
- (a^m)^n = a^(m×n)
- a^0 = 1 (any non-zero number)
- a^(−n) = 1/a^n
Fractional Exponents
a^(1/2) = √a (square root). a^(1/3) = ∛a (cube root). a^(m/n) = ⁿ√(a^m).
Order of Operations Reminder
Exponents are calculated before multiplication, division, addition, and subtraction (the "E" in PEMDAS) — a frequent source of calculation errors. −3² equals −9 (square 3, then negate), while (−3)² equals 9 (negate first, then square) — the parentheses completely change the answer.
Scientific Notation
Exponents make very large or small numbers manageable: 6.022 × 10²³ (Avogadro's number) instead of writing 23 digits. Moving the decimal point right decreases the exponent; moving it left increases it — the exponent always reflects how many places the decimal shifted from standard form.