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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. 8.41 (page 765)

Simplify:
$(a) \sqrt{\frac{a^{8}}{a^{6}}} (b) \sqrt[4]{\frac{x^{7}}{x^{3}}} (c) \sqrt[4]{\frac{y^{17}}{y^{5}}}$

Short Answer

Expert verified

Part a. After simplifying we get, $a .$

Part b. After simplifying we get, $x .$

Part c. After simplifying we get, $y^{3} .$

Step by step solution

01

Part a Step 1. Given Information

The given expression is $\sqrt{\frac{a^{8}}{a^{6}}} .$

We have to simplify it.

02

Part a Step 2. Use the Quotient Property of exponents to simplify

By using the property we get,

$\sqrt{\frac{a^{8}}{a^{6}}} = \sqrt{a^{8 - 6}} = \sqrt{a^{2}} = a$

03

Part b Step 1. Given Information

The given expression is $\sqrt[4]{\frac{x^{7}}{x^{3}}} .$

We have to simplify it.

04

Part b Step 2. Use the Quotient Property of exponents to simplify

By using the property we get,

$\sqrt[4]{\frac{x^{7}}{x^{3}}} = \sqrt[4]{x^{7 - 3}} = \sqrt[4]{x^{4}} = x$

05

Part c Step 1. Given Information

The given expression is $\sqrt[4]{\frac{y^{17}}{y^{5}}} .$

We have to simplify it.

06

Part c Step 2. Use the Quotient Property of exponents to simplify

By using the property we get,

$\sqrt[4]{\frac{y^{17}}{y^{5}}} = \sqrt[4]{y^{17 - 5}} = \sqrt[4]{y^{12}} = \sqrt[4]{{(y^{3})}^{4}} = y^{3}$

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Most popular questions from this chapter

In the following exercises, use the Product Property to simplify radical expression $\sqrt{125} .$

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