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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.416. (page 560)

Simplify the expression using the quotient to a power property.
${(\frac{4 p^{- 3}}{q^{2}})}^{2}$

Short Answer

Expert verified

The solution is $\frac{16}{p^{6} q^{4}}$ .

Step by step solution

01

Step 1. Given information.

The given expression is ${(\frac{4 p^{- 3}}{q^{2}})}^{2}$ .

02

Step 2. Simplify the expression.

Solve it as follows:

${(\frac{4 p^{- 3}}{q^{2}})}^{2} = \frac{{(4 p^{- 3})}^{2}}{{(q^{2})}^{2}} {(\frac{4 p^{- 3}}{q^{2}})}^{2} = \frac{4^{2} {(p^{- 3})}^{2}}{q^{4}} {(\frac{4 p^{- 3}}{q^{2}})}^{2} = \frac{16 p^{- 6}}{q^{4}} {(\frac{4 p^{- 3}}{q^{2}})}^{2} = \frac{16}{p^{6} q^{4}}$

03

Step 3. Simplified answer.

Hence, the simplified expression is $\frac{16}{p^{6} q^{4}}$ .

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Find the product of the below expression.

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