Chapter 8: Q. 149 (page 787)

In the following exercises, simplify.
(a) $- 9^{\frac{3}{2}}$
(b) $- 9^{- \frac{3}{2}}$
(c) ${(- 9)}^{\frac{3}{2}}$

Short Answer

Expert verified

(a) The answer is $- 27$

(b) The answer is $- \frac{1}{27}$

Step by step solution

Step 1. Part (a) Simplify the expression -932

$- {(9)}^{\frac{3}{2}} = - {(\sqrt{9})}^{3} = - {(3)}^{3} = - 27$

Step 2. Part (b) Simplify the expression -9-32

$- {(9)}^{- \frac{3}{2}} = - {(\sqrt{9})}^{- 3} = - {(3)}^{- 3} = - \frac{1}{3^{3}} = - \frac{1}{27}$

Step 3. Part (c) Simplify the expression -932

${(- 9)}^{\frac{3}{2}} {(\sqrt{- 9})}^{3}$

This is not a real solution.

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.

In the following exercises, simplify.
(a) $- 9^{\frac{3}{2}}$
(b) $- 9^{- \frac{3}{2}}$
(c) ${(- 9)}^{\frac{3}{2}}$

Short Answer

Step by step solution

Step 1. Part (a) Simplify the expression -932

Step 2. Part (b) Simplify the expression -9-32

Step 3. Part (c) Simplify the expression -932

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Geometry

Calculus

Statistics

Theoretical and Mathematical Physics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify.(a) -932(b) -9-32(c)-932

Short Answer

Step by step solution

Step 1. Part (a) Simplify the expression -932

Step 2. Part (b) Simplify the expression -9-32

Step 3. Part (c) Simplify the expression -932

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Geometry

Calculus

Statistics

Theoretical and Mathematical Physics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify.
(a) $- 9^{\frac{3}{2}}$
(b) $- 9^{- \frac{3}{2}}$
(c) ${(- 9)}^{\frac{3}{2}}$