EDGE Math 8

Positive Integer Exponents

Example 2

Evaluate each expression.

a. $3^{2} \cdot 2$

b. $(- 3) \cdot 2^{4}$

c. $5^{2} \cdot {(- 2)}^{3}$

d. $2^{2} + 5^{2}$

Solution

Use the definition of a positive integer exponent.

a. $3^{2} \cdot 2 = 3 \cdot 3 \cdot 2 = 9 \cdot 2 = 18$

(- 3) \cdot 2^{4} = (- 3) \cdot 2 \cdot 2 \cdot 2 \cdot 2

= (- 3) \cdot 16 = - 48

5^{2} \cdot {(- 2)}^{3} = 5 \cdot 5 \cdot (- 2) (- 2) (- 2)

= (25) (- 8) = - 200

2^{2} + 5^{2} = 2 \cdot 2 + 5 \cdot 5

= 4 + 25 = 29

Take note that when you are raising a negative number to a power, you need to enclose the negative number in parentheses; for example, ${(- 2)}^{4} = 16 .$ Notice that in the expression $- 2^{4},$ you are not raising $- 2$ to the 4th power; instead, the expression means that $- 2^{4} = (- 1) \cdot 2^{4} = - 16 .$