Chapter 8: Q. 143 (page 787)

In the following exercises, write with a rational exponent.
$(a) \sqrt[5]{u^{2}} (b) (\sqrt[3]{6 x})^{5} (c) \sqrt[4]{{(\frac{18 a}{5 b})}^{7}}$

Short Answer

Expert verified

(a) The answer is $u^{\frac{2}{5}}$

(b) The answer is ${(6 x)}^{\frac{5}{3}}$

Step by step solution

Step 1. Part (a) Simplify the expression u25

We will use the property

$a^{\frac{m}{n}} = (\sqrt[n]{a})^{m}$ and $a^{\frac{m}{n}} = \sqrt[n]{a^{m}}$

$\sqrt[5]{u^{2}} = {(u^{2})}^{\frac{1}{5}} = u^{\frac{2}{5}}$

Step 2. Part (b) Simplify the expression (6x3)5

${(\sqrt[3]{6 x})}^{5} = {({(6 x)}^{\frac{1}{3}})}^{5} = {(6 x)}^{\frac{5}{3}}$

Step 3. Part (c) Simplify the expression 18a5b74

$\sqrt[4]{{(\frac{18 a}{5 b})}^{7}} = {(\frac{18 a}{5 b})}^{\frac{7}{4}}$

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In the following exercises, write with a rational exponent.
$(a) \sqrt[5]{u^{2}} (b) (\sqrt[3]{6 x})^{5} (c) \sqrt[4]{{(\frac{18 a}{5 b})}^{7}}$

Short Answer

Step by step solution

Step 1. Part (a) Simplify the expression u25

Step 2. Part (b) Simplify the expression (6x3)5

Step 3. Part (c) Simplify the expression 18a5b74

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In the following exercises, write with a rational exponent.(a)u25(b)(6x3)5(c)18a5b74

Short Answer

Step by step solution

Step 1. Part (a) Simplify the expression u25

Step 2. Part (b) Simplify the expression (6x3)5

Step 3. Part (c) Simplify the expression 18a5b74

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Mechanics Maths

Calculus

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Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In the following exercises, write with a rational exponent.
$(a) \sqrt[5]{u^{2}} (b) (\sqrt[3]{6 x})^{5} (c) \sqrt[4]{{(\frac{18 a}{5 b})}^{7}}$