Definition
Power
A power is a base raised to an exponent, such as 3⁴.
What it means
In 3⁴, the 3 is the base—the number being repeated. The raised 4 is the exponent—it tells you there are four factors of 3. So 3⁴ = 3 × 3 × 3 × 3 = 81. This repeated-factor picture is for positive whole-number exponents; zero and negative exponents follow additional rules.
Remember it
The small raised exponent counts factors; the base is the factor that repeats.
Example
Read 5³ as “five to the third power.” Expand it as 5 × 5 × 5, then calculate 25 × 5 = 125. The power 5³ has base 5, exponent 3, and value 125.
Watch for
On this page, power means the whole exponent expression aⁿ. Some books also use “power” loosely for the exponent or the result, so check the surrounding words.
Common mix-up
The exponent is not a number to multiply by the base: 4³ means 4 × 4 × 4, not 4 × 3.
Exact meaning
A power is an expression of the form aⁿ, with a base and an exponent. When n is a positive whole number, aⁿ means a used as a factor n times.