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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. 5.32 (page 508)

Simplify each expression:
$鈸� {(\frac{3}{5})}^{鈭� 3} 鈸� {(- \frac{a}{b})}^{鈭� 4}$

Short Answer

Expert verified

The simplified expression of ${(\frac{3}{5})}^{鈭� 3} = \frac{125}{27}$

The simplified expression of ${(- \frac{a}{b})}^{鈭� 4} = \frac{b^{4}}{a^{4}}$

Step by step solution

01

Step 1. Given Information

In the given question we have to simplify each expression:

$鈸� {(\frac{3}{5})}^{鈭� 3} 鈸� {(- \frac{a}{b})}^{鈭� 4}$

02

Part (a) Step 1. The given expression is 35−3

Quotient to a Negative Power Property

If $a$ and $b$ are real numbers, $a 鈮� 0, b 鈮� 0$ and n is an integer, then ${(\frac{a}{b})}^{鈭� n} = {(\frac{b}{a})}^{n}$

03

Part (a) Step 2. The expression is 35−3

Using the Quotient to a Negative Exponent Property,

Take the reciprocal of the fraction and change the sign of the exponent.

${(\frac{3}{5})}^{鈭� 3} = {(\frac{5}{3})}^{3}$

Simplifying

${(\frac{3}{5})}^{鈭� 3} = \frac{5^{3}}{3^{3}}$

${(\frac{3}{5})}^{鈭� 3} = \frac{125}{27}$

04

Part (b) Step 1. The given expression is -ab−4

Quotient to a Negative Power Property

If $a$ and $b$ are real numbers, $a 鈮� 0, b 鈮� 0$ and n is an integer, then ${(\frac{a}{b})}^{鈭� n} = {(\frac{b}{a})}^{n}$

05

Part (b) Step 2. The expression is -ab−4

Using the Quotient to a Negative Exponent Property,

Take the reciprocal of the fraction and change the sign of the exponent.

${(- \frac{a}{b})}^{鈭� 4} = {(- \frac{b}{a})}^{4}$

Simplifying

${(- \frac{a}{b})}^{鈭� 4} = \frac{b^{4}}{a^{4}}$

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