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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. 63 (page 771)

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

Short Answer

Expert verified

The expression in simplified form is $2 \sqrt[4]{2}, 2 \sqrt[5]{2}$ respectively

Step by step solution

01

Given information

Given the expression $\sqrt[4]{32}, \sqrt[5]{64}$

02

Using the product property to simplify

Using the property, we get

$\sqrt[4]{32} = \sqrt[4]{16 路 2} \sqrt[4]{32} = = 2 路 \sqrt[4]{2} \sqrt[4]{32} = = 2 \sqrt[4]{2}$

03

Simplifying for another expression

Using the property, we get

$\sqrt[5]{64} = \sqrt[5]{32 路 2} \sqrt[5]{64} = 2 路 \sqrt[5]{2} \sqrt[5]{64} = 2 \sqrt[5]{2}$

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Most popular questions from this chapter

Use the Quotient Property to simplify square roots.

(a) $\sqrt{\frac{50 r^{5} s^{2}}{128 r^{2} s^{6}}}$

(b) $\sqrt[3]{\frac{24 m^{9} n^{7}}{375 m^{4} n}}$

(c) $\sqrt[4]{\frac{81 m^{2} n^{8}}{256 m n^{2}}}$

In the following exercises, simplify using absolute value signs as needed. $\sqrt{147 m^{7} n^{11}}, \sqrt[3]{48 x^{6} y^{7}}, \sqrt[4]{32 x^{5} y^{4}}$

In the following exercises, write with a rational exponent.

$鈸� \sqrt[8]{r} 鈸� \sqrt[10]{s} 鈸� \sqrt[4]{t}$

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 exercise, write as a radical expression.

鈸� x^{\frac{1}{2}} 鈸� y^{\frac{1}{3}} 鈸� z^{\frac{1}{4}}

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