What is a power?

Repeated multiplication

A power is a shorthand way of writing the multiplication of a number by itself, repeated several times in succession.

a^n = a × a × a × … × a (n factors)

a is called the base and n the exponent.

Example

2^4 = 2 × 2 × 2 × 2 = 16

This is read as ‘2 to the power of 4’ or ‘2 raised to the power of 4’.

Notation	Expansion	Result
3^2	3 × 3	9
5^3	5 × 5 × 5	125
10²	10 × 10	100

Special cases

• a¹ = a (a raised to the power of 1 is the same as a)
• a⁰ = 1, for any a not equal to 0

Powers of 10

These are very useful: 10^n is written as a 1 followed by n zeros.

10^1 = 10, 10^2 = 100, 10^3 = 1000, 10^6 = 1 000 000

Common pitfalls

• Do not confuse a^n with a × n. For example, 2^3 = 2 × 2 × 2 = 8, not 2 × 3 = 6.
• Be careful with signs: (-2)² = (-2) × (-2) = 4, but -2² = -(2²) = -4 because the exponent only applies to the 2, not to the minus sign in front of it.
• (-2)^3 = -8 (odd exponent, the sign remains negative), whereas (-2)^2 = 4 (even exponent, the result becomes positive).