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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. 68 (page 771)

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

Short Answer

Expert verified

The expression in simplified form is $m \sqrt[6]{m}, u \sqrt[5]{u^{2}}, v \sqrt[6]{v^{5}}$

Step by step solution

01

Given information

Given the expression $\sqrt{m^{13}}, \sqrt[5]{u^{7}}, \sqrt[6]{v^{11}}$

02

Using the product property

Using the product property, we get

$\sqrt{m^{13}} = \sqrt{m^{12} m} \sqrt{m^{13}} = \sqrt{m^{12}} \sqrt{m} \sqrt{m^{13}} = m^{6} \sqrt{m}$ m

03

Using the product property

Using the property, we get

$\sqrt[5]{u^{7}} = = \sqrt[5]{u^{5} u^{2}} \sqrt[5]{u^{7}} = \sqrt[5]{u^{5}} \sqrt[5]{u^{2}} \sqrt[5]{u^{7}} = u \sqrt[5]{u^{2}}$

04

Using the property

Using the property, we have

$\sqrt[6]{v^{11}} = \sqrt[6]{v^{6} v^{5}} \sqrt[6]{v^{11}} = \sqrt[6]{v^{6}} \sqrt[6]{v^{5}} \sqrt[6]{v^{11}} = v \sqrt[6]{v^{5}}$

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Most popular questions from this chapter

In the following exercises, simplify.

(a) $25^{\frac{3}{2}}$

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

(c) ${(- 64)}^{\frac{2}{3}}$

In the following exercises, simplify.

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

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

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

In the following exercises, solve.
$\sqrt{v - 10} + 10 = v$

In the following exercises, write with a rational exponent.

$(a) \sqrt[5]{u^{2}} (b) (\sqrt[3]{6 x})^{5} (c) \sqrt[4]{{(\frac{18 a}{5 b})}^{7}}$

In the following exercises, use the Product Property to simplify radical expressions a. $\sqrt[4]{32}$ ,b. $\sqrt[5]{64}$

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