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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. 152 (page 787)

In the following exercises, simplify.
(a) $6^{\frac{5}{2}} 路 6^{\frac{1}{2}}$
(b) ${(b^{15})}^{\frac{3}{5}}$
(c) $\frac{w^{\frac{2}{7}}}{w^{\frac{9}{7}}}$

Short Answer

Expert verified

(a) The answer is $216$

(b) The answer is $b^{9}$

(c) The answer is $\frac{1}{w}$

Step by step solution

01

Step 1. Part (a) Simplify the expression 652·612

We will use the property

$a^{m} 路 a^{n} = a^{m + n}$

6^{\frac{5}{2}} 路 6^{\frac{1}{2}} = 6^{\frac{5}{2} + \frac{1}{2}} = 6^{\frac{6}{2}} = 6^{3} = 216

02

Step 2. Part (b) Simplify the expression b1535

We will use the property

${(a^{m})}^{n} = a^{m n}$

{(b^{15})}^{\frac{3}{5}} = b^{15 脳 \frac{3}{5}} = b^{9}

03

Step 3. Part (c) Simplify the expression w27w97

We will use the property

$\frac{a^{m}}{a^{n}} = a^{m - n}$

\frac{w^{\frac{2}{7}}}{w^{\frac{9}{7}}} = w^{\frac{2}{7} - \frac{9}{7}} = w^{- \frac{7}{7}} = w^{- 1} = \frac{1}{w}

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Most popular questions from this chapter

Explain why $\sqrt[4]{- 64}$ is not a real number but $\sqrt[3]{- 64}$ is.

In the following exercises, simplify using absolute value signs as needed. $\sqrt{m^{13}}, \sqrt[5]{u^{7}}, \sqrt[6]{v^{11}}$

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