EDGE Math 8

Negative Exponents

Example 2

Simplify each expression. Assume that the variables represent nonzero real numbers.

a. $y^{8} \cdot y^{- 3}$

b. $x^{7} \cdot x^{- 10}$

c. ${(2^{- 2} y^{- 4})}^{2}$

Solution

a. $y^{8} \cdot y^{- 3} = y^{8 + (- 3)} = y^{5}$

b. $x^{7} \cdot x^{- 10} = x^{7 + (- 10)} = x^{- 3} = \frac{1}{x^{3}}$

c. ${(2^{- 2} y^{- 4})}^{2} = {(2^{- 2})}^{2} {(y^{- 4})}^{2} = 2^{- 4} y^{- 8}$

= \frac{1}{2^{4} y^{8}} = \frac{1}{16 y^{8}}