Q. 77 In the following exercises, simp... [FREE SOLUTION]

91影视

Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 8: Q. 77 (page 771)

In the following exercises, simplify using absolute value signs as needed. $\sqrt{192 q^{3} r^{7}}, \sqrt[3]{54 m^{9} n^{10}}, \sqrt[4]{81 a^{9} b^{8}}$

Short Answer

Expert verified

The expression in simplified form is $8 |q r^{3}| \sqrt{3 q r}, 3 m^{3} n^{3} \sqrt[3]{2 n}, 3 a^{2} b^{2} \sqrt[4]{a}$ respectively

Step by step solution

Given information

Given the expression $\sqrt{192 q^{3} r^{7}}, \sqrt[3]{54 m^{9} n^{10}}, \sqrt[4]{81 a^{9} b^{8}}$

Using the product property

Using the property, we get

$\sqrt{192 q^{3} r^{7}} = \sqrt{64 q^{2} r^{6} 路 3 q r} \sqrt{192 q^{3} r^{7}} = \sqrt{{(8 q r^{3})}^{2} 路 3 q r} \sqrt{192 q^{3} r^{7}} = \sqrt{{(8 q r^{3})}^{2}} 路 \sqrt{3 q r} \sqrt{192 q^{3} r^{7}} = 8 |q r^{3}| \sqrt{3 q r}$

Using the product property

Using the property, we get

$\sqrt[3]{54 m^{9} n^{10}} = \sqrt[3]{27 m^{9} n^{9} 路 2 n} \sqrt[3]{54 m^{9} n^{10}} = \sqrt[3]{{(3 m^{3} n^{3})}^{3} 路 2 n} \sqrt[3]{54 m^{9} n^{10}} = \sqrt[3]{{(3 m^{3} n^{3})}^{3}} 路 \sqrt[3]{2 n} \sqrt[3]{54 m^{9} n^{10}} = 3 m^{3} n^{3 .} \sqrt[3]{2 n}$

Using the product property

Using the property, we get

$\sqrt[4]{81 a^{9} b^{8}} = \sqrt[4]{81 a^{8} b^{8} 路 a} \sqrt[4]{81 a^{9} b^{8}} = \sqrt[4]{{(3 a^{2} b^{2})}^{4} 路 a} \sqrt[4]{81 a^{9} b^{8}} = = \sqrt[4]{{(3 a^{2} b^{2})}^{4}} 路 \sqrt[4]{a} \sqrt[4]{81 a^{9} b^{8}} = 3 |a^{2} b^{2}| . \sqrt[4]{a} \sqrt[4]{81 a^{9} b^{8}} = 3 a^{2} b^{2} . \sqrt[4]{a}$

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91影视

In the following exercises, simplify using absolute value signs as needed. $\sqrt{192 q^{3} r^{7}}, \sqrt[3]{54 m^{9} n^{10}}, \sqrt[4]{81 a^{9} b^{8}}$

Short Answer

Step by step solution

Given information

Using the product property

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.192q3r7,54m9n103,81a9b84

Short Answer

Step by step solution

Given information

Using the product property

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

Calculus

Geometry

Probability and Statistics

Applied Mathematics

Pure Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify using absolute value signs as needed. $\sqrt{192 q^{3} r^{7}}, \sqrt[3]{54 m^{9} n^{10}}, \sqrt[4]{81 a^{9} b^{8}}$