Lesson 1: Understand and Represent Exponents

Property

An exponent is a number that appears above and to the right of a particular factor. It tells us how many times that factor occurs in the expression. The factor to which the exponent applies is called the base, and the product is called a power of the base.
An exponent indicates repeated multiplication.

where $n$ is a positive integer.

Examples

• To compute $5^3$, we multiply three factors of 5: $5 \cdot 5 \cdot 5 = 125$.

• The expression $(\frac{1}{4})^2$ means $\frac{1}{4} \cdot \frac{1}{4} = \frac{1}{16}$.

Property

For any non-zero number $a$, a number raised to the power of zero is equal to 1.

Examples

Property

The rule of repeated multiplication applies to any base, including decimals and fractions. For a fractional base, the exponent applies to both the numerator and the denominator.

Examples