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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. 497 (page 851)

In the following exercises, simplify using absolute value signs as needed.
$(a) \sqrt{80 s^{15}} (b) \sqrt[5]{96 a^{7}} (c) \sqrt[6]{128 b^{7}}$

Short Answer

Expert verified

The required answer are $4 s^{7} \sqrt{5 s}, 2 a \sqrt[5]{3 a^{2}} a n d 2 b \sqrt[6]{2 b}$

Step by step solution

01

Step 1. Given Information

The given expression is

$(a) \sqrt{80 s^{15}} (b) \sqrt[5]{96 a^{7}} (c) \sqrt[6]{128 b^{7}}$

02

Part(a) Step 1. Calculation

Simplify the expression using product property.

$\sqrt{80 s^{15}} = \sqrt{16 s^{14}} 脳 \sqrt{5 s} = \sqrt{{(4 s^{7})}^{2}} 脳 \sqrt{5 s} = 4 s^{7} \sqrt{5 s}$

03

Part(b) Step 1. Calculation

Simplify the expression using product property.

$\sqrt[5]{96 a^{7}} = \sqrt[5]{32 a^{5}} 脳 \sqrt[5]{3 a^{2}} = \sqrt[5]{{(2 a)}^{5}} 脳 \sqrt[5]{3 a^{2}} = 2 a \sqrt[5]{3 a^{2}}$

04

Part(c) Step 1. Calculation

Simplify the expression using product property.

$\sqrt[6]{128 b^{7}} = \sqrt[6]{64 b^{6}} 脳 \sqrt[6]{2 b} = \sqrt[6]{{(2 b)}^{6}} 脳 \sqrt[6]{2 b} = 2 b \sqrt[6]{2 b}$

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Most popular questions from this chapter

Explain how you know that

$\sqrt[5]{x^{10}} = x^{2}$

In the following exercises, use the Product Property to simplify radical expressions a $\sqrt[5]{64}$ , b. $\sqrt[3]{256}$

Simplify:

$(a) 5 + \sqrt{75} (b) \frac{10 - \sqrt{75}}{5} .$

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, write with a rational exponent.

$\sqrt[3]{7 c} 鈸� \sqrt[7]{12 d} 鈸� 2 \sqrt[4]{6 b}$

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