EDGE Math 8

Positive Integer Exponents

A positive integer exponent indicates the number of times the base is used as a factor in the product. Thus, raising a number to an exponent (also called exponentiation) may be thought of as repeated multiplication.

Definition

If $n$ is a positive integer and $a$ is a real number, then

a^{n} = \underset{n times}{\underset{︸}{a \times a \times a \times \dots \times a}} .

Example 1

Evaluate each expression.

a. $2^{3}$

b. ${(- 2)}^{5}$

c. $4^{1}$

d. ${(\frac{1}{3})}^{2}$

Solution

Use the definition of a positive integer exponent.

a. $2^{3} = 2 \times 2 \times 2 = 8$

{(- 2)}^{5}

= (- 2) \times (- 2) \times (- 2)

\times (- 2) \times (- 2)

= - 32

c. $4^{1} = 4$

d. ${(\frac{1}{3})}^{2} = \frac{1}{3} \times \frac{1}{3} = \frac{1}{3 \times 3} = \frac{1}{9}$