Q 729 In the following exercises, simp... [FREE SOLUTION]

91影视

Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 9: Q 729 (page 1152)

In the following exercises, simplify
$(a) \sqrt[5]{64 c^{8}} . (b) \sqrt[4]{48 d^{7}} .$

Short Answer

Expert verified

The simplification of the expressions are:

$(a) \sqrt[5]{64 c^{8}} = 2 c \sqrt[5]{2 c^{3}} . (b) \sqrt[4]{48 d^{7}} = 2 d \sqrt[4]{3 d^{3}} .$

Step by step solution

Part (a) Step 1. Given information

The given expression is $\sqrt[5]{64 c^{8}} .$

Part (a) Step 2. Simplification

$\sqrt[5]{64 c^{8}} = \sqrt[5]{2^{6} c^{5 + 3}} = \sqrt[5]{2^{5 + 1} c^{5 + 3}} = \sqrt[5]{2^{5} 脳 2^{1} c^{5} 脳 c^{3}} = \sqrt[5]{2^{5} 脳 2 c^{5} 脳 c^{3}} = \sqrt[5]{2^{5}} 脳 \sqrt[5]{c^{5}} 脳 \sqrt[5]{2 c^{3}} = {(2^{5})}^{\frac{1}{5}} 脳 {(c^{5})}^{\frac{1}{5}} 脳 {(2 c^{3})}^{\frac{1}{5}} = 2 c \sqrt[5]{2 c^{3}} H e n c e, \sqrt[5]{64 c^{8}} = 2 c \sqrt[5]{2 c^{3}}$

Part (b) Step 1. Given information

The given expression is $\sqrt[4]{48 d^{7}} .$

Part (b) Step 2. Simplification

$\sqrt[4]{48 d^{7}} = \sqrt[4]{2^{4} 脳 3 d^{4 + 3}} = \sqrt[4]{2^{4} 脳 3 d^{4} 脳 d^{3}} = \sqrt[4]{2^{4}} \sqrt[4]{d^{4}} \sqrt[4]{3 d^{3}} = {(2^{4})}^{\frac{1}{4}} 脳 {(d^{4})}^{\frac{1}{4}} 脳 {(3 d^{3})}^{\frac{1}{4}} = 2 d \sqrt[4]{3 d^{3}} H e n c e, \sqrt[4]{48 d^{7}} = 2 d \sqrt[4]{3 d^{3}}$

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91影视

In the following exercises, simplify
$(a) \sqrt[5]{64 c^{8}} . (b) \sqrt[4]{48 d^{7}} .$

Short Answer

Step by step solution

Part (a) Step 1. Given information

Part (a) Step 2. Simplification

Part (b) Step 1. Given information

Part (b) Step 2. Simplification

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91影视

In the following exercises, simplify(a)64c85.(b)48d74.

Short Answer

Step by step solution

Part (a) Step 1. Given information

Part (a) Step 2. Simplification

Part (b) Step 1. Given information

Part (b) Step 2. Simplification

One App. One Place for Learning.

Most popular questions from this chapter

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In the following exercises, simplify
$(a) \sqrt[5]{64 c^{8}} . (b) \sqrt[4]{48 d^{7}} .$