EDGE Math 8

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Zero and Negative Integer Exponents

Negative Exponents

Example 3

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

a. $\frac{2 b^{- 6} c^{2}}{9 b^{3} c^{5}}$

b. ${(\frac{p^{2} q^{3}}{6 p^{5} q})}^{- 2}$

Solution

a.	$\frac{2 b^{- 6} c^{2}}{9 b^{3} c^{5}}$	$= \frac{2}{9} \cdot \frac{b^{- 6}}{b^{3}} \cdot \frac{c^{2}}{c^{5}}$
		$= \frac{2}{9} \cdot b^{- 6 - 3} \cdot c^{2 - 5}$
		$= \frac{2}{9} b^{- 9} c^{- 3}$
		$= \frac{2}{9} \cdot \frac{1}{b^{9}} \cdot \frac{1}{c^{3}}$
		$= \frac{2}{9 b^{9} c^{3}}$

b.	${(\frac{p^{2} q^{3}}{6 p^{5} q})}^{- 2}$	$= \frac{p^{- 4} q^{- 6}}{6^{- 2} p^{- 10} q^{- 2}}$
		$= \frac{1}{6^{- 2}} \cdot \frac{p^{- 4}}{p^{- 10}} \cdot \frac{q^{- 6}}{q^{- 2}}$
		$= 6^{2} p^{- 4 - (- 10)} q^{- 6 - (- 2)}$
		$= 36 p^{- 4 + 10} q^{- 6 + 2}$
		$= 36 p^{6} q^{- 4}$
		$= 36 p^{6} \cdot \frac{1}{q^{4}}$
		$= \frac{36 p^{6}}{q^{4}}$