Q. 70 In the following exercises, simp... [FREE SOLUTION]

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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. 70 (page 771)

In the following exercises, simplify using absolute value signs as needed. $\sqrt{r^{25}}, \sqrt[5]{p^{8}}, \sqrt[4]{m^{5}}$

Short Answer

Expert verified

The expression in simplified form is $r^{12} \sqrt{r}, p \sqrt[5]{p^{3}}, | m | \sqrt[4]{m}$ respectively

Step by step solution

Given information

Given the expression $\sqrt{r^{25}}, \sqrt[5]{p^{8}}, \sqrt[4]{m^{5}}$

Using the product property

Using the product property, we get

$\sqrt{r^{25}} = \sqrt{{(r^{12})}^{2} 路 r^{1}} \sqrt{r^{25}} = \sqrt{{(r^{12})}^{2} 路 r} \sqrt{r^{25}} = \sqrt{{(r^{12})}^{2}} 路 \sqrt{r} \sqrt{r^{25}} = |r^{12}| \sqrt{r} \sqrt{r^{25}} = r^{12} \sqrt{r}$

Step 3; Using the product property

Using the property, we get

$\sqrt[5]{p^{8}} = \sqrt[5]{p^{5} 路 p^{3}} \sqrt[5]{p^{8}} = = \sqrt[5]{p^{5}} 路 \sqrt[5]{p^{3}} \sqrt[5]{p^{8}} = p \sqrt[5]{p^{3}}$

Using the product property

Using the property, we get

$\sqrt[4]{m^{5}} = \sqrt[4]{{(m^{1})}^{4} 路 m^{1}} \sqrt[4]{m^{5}} = \sqrt[4]{{(m^{1})}^{4} 路 m} \sqrt[4]{m^{5}} = \sqrt[4]{{(m^{1})}^{4}} 路 \sqrt[4]{m} \sqrt[4]{m^{5}} = | m | \sqrt[4]{m}$

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91影视

In the following exercises, simplify using absolute value signs as needed. $\sqrt{r^{25}}, \sqrt[5]{p^{8}}, \sqrt[4]{m^{5}}$

Short Answer

Step by step solution

Given information

Using the product property

Step 3; Using the product property

Using the product property

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91影视

In the following exercises, simplify using absolute value signs as needed.r25,p85,m54

Short Answer

Step by step solution

Given information

Using the product property

Step 3; Using the product property

Using the product property

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Decision Maths

Applied Mathematics

Theoretical and Mathematical Physics

Discrete Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify using absolute value signs as needed. $\sqrt{r^{25}}, \sqrt[5]{p^{8}}, \sqrt[4]{m^{5}}$