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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 5: Q.403. (page 560)

Simplify the expression by using the product property.
$(u v^{- 3}) (u^{- 4} v^{- 2})$

Short Answer

Expert verified

The solution is $\frac{1}{u^{3} v^{5}}$ .

Step by step solution

01

Step 1. Given information.

The given expression is $(u v^{- 3}) (u^{- 4} v^{- 2})$ .

02

Step 2. Simplify the expression.

Solve it as follows:
$(u v^{- 3}) (u^{- 4} v^{- 2}) = u 路 u^{- 4} 路 v^{- 3} 路 v^{- 2} (u v^{- 3}) (u^{- 4} v^{- 2}) = u^{1 - 4} 路 v^{- 3 - 2} (u v^{- 3}) (u^{- 4} v^{- 2}) = u^{- 3} 路 v^{- 5} (u v^{- 3}) (u^{- 4} v^{- 2}) = \frac{1}{u^{3} v^{5}}$

03

Step 3. Simplified answer.

Hence, the simplified expression is $\frac{1}{u^{3} v^{5}}$ .

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