Chapter 11: Q. 5.31 (page 1069)

Simplify each expression:
$ⓐ {(\frac{2}{3})}^{- 4} ⓑ {(- \frac{m}{n})}^{- 2}$

Short Answer

Expert verified

The simplified expression of ${(\frac{2}{3})}^{- 4} = \frac{81}{16}$

The simplified expression oflocalid="1661181245341" ${(- \frac{m}{n})}^{- 2} = \frac{n^{2}}{m^{2}}$

Step by step solution

Step 1. Given Information

In the given question we have to simplify each expression:

$ⓐ {(\frac{2}{3})}^{- 4} ⓑ {(- \frac{m}{n})}^{- 2}$

Part (a) Step 1. The given expression is 23−4

Quotient to a Negative Power Property

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

Part (a) Step 2. The expression is 23−4

Using the Quotient to a Negative Exponent Property,

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

${(\frac{2}{3})}^{- 4} = {(\frac{3}{2})}^{4}$

Simplifying

${(\frac{2}{3})}^{- 4} = \frac{3^{4}}{2^{4}}$

${(\frac{2}{3})}^{- 4} = \frac{81}{16}$

Part (b) Step 1. The given expression is -mn−2

Quotient to a Negative Power Property

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

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

Using the Quotient to a Negative Exponent Property,

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

${(- \frac{m}{n})}^{- 2} = {(- \frac{n}{m})}^{2}$

Simplifying

${(- \frac{m}{n})}^{- 2} = \frac{n^{2}}{m^{2}}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Simplify each expression:
$ⓐ {(\frac{2}{3})}^{- 4} ⓑ {(- \frac{m}{n})}^{- 2}$

Short Answer

Step by step solution

Step 1. Given Information

Part (a) Step 1. The given expression is 23−4

Part (a) Step 2. The expression is 23−4

Part (b) Step 1. The given expression is -mn−2

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Pure Maths

Logic and Functions

Mechanics Maths

Applied Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

Simplify each expression:ⓐ23−4ⓑ-mn−2

Short Answer

Step by step solution

Step 1. Given Information

Part (a) Step 1. The given expression is 23−4

Part (a) Step 2. The expression is 23−4

Part (b) Step 1. The given expression is -mn−2

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Pure Maths

Logic and Functions

Mechanics Maths

Applied Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

Simplify each expression:
$ⓐ {(\frac{2}{3})}^{- 4} ⓑ {(- \frac{m}{n})}^{- 2}$