Exponent

Definition

An exponent indicates how many times a number, known as the base, is multiplied by itself. It is written as a small number to the upper right of the base.

5 Must Know Facts For Your Next Test

1. The expression $a^n$ means 'a' raised to the power of 'n'.
2. Any non-zero number raised to the zero power equals 1 ($a^0 = 1$).
3. A negative exponent represents a reciprocal; for example, $a^{-n} = \frac{1}{a^n}$.
4. Exponents follow specific rules such as the product rule ($a^m \cdot a^n = a^{m+n}$) and the power rule ($(a^m)^n = a^{mn}$).
5. For any positive integer n, $10^n$ gives a 1 followed by n zeros.

Review Questions

• What does $2^3$ equal?
• How do you express $\frac{1}{4}$ using an exponent?
• What is the result of $(3^2)^3$?

Related terms

Base:

The number that is being multiplied by itself in an expression with an exponent.

Reciprocal:

The inverse of a number; for instance, the reciprocal of 'a' is $\frac{1}{a}$.

Power Rule:

$(a^m)^n = a^{mn}$; it states that when raising an exponential expression to another power, you multiply the exponents.