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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

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 $- \frac{1}{27}$

(c) The answer is Not real solution.

Step by step solution

01

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

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

02

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

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

03

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

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

This is not a real solution.

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Most popular questions from this chapter

Use the Quotient Property to simplify square roots.

(a) $\sqrt{\frac{32 x^{5} y^{3}}{18 x^{3} y}}$

(b) $\sqrt[3]{\frac{5 x^{6} y^{9}}{40 x^{5} y^{3}}}$

(c) $\sqrt[4]{\frac{5 a^{8} b^{6}}{80 a^{3} b^{2}}}$

In the following exercises, simplify using absolute value signs as needed. $\sqrt{175 n^{13}}, \sqrt[5]{512 p^{5}}, \sqrt[4]{324 q^{7}}$

Write as a radical expression:

(a) $t^{\frac{1}{2}}$

(b) $m^{\frac{1}{3}}$

(c) $r^{\frac{1}{4}}$

Write with a rational exponent:

(a) $\sqrt[5]{a^{2}}$

(b) ${(\sqrt[3]{5 a b})}^{5}$

(c) $\sqrt{{(\frac{7 x y}{z})}^{3}}$

Simplify:

a. ${(81 n^{\frac{2}{5}})}^{\frac{3}{2}}$ b. ${(a^{\frac{3}{2}} b^{\frac{1}{2}})}^{\frac{4}{3}}$

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