Chapter 8: Q. 127 (page 786)

In the following exercises, write with a rational exponent.
$ⓐ \sqrt{21 p} ⓑ \sqrt[4]{48 q} ⓒ 4 \sqrt[6]{36 r}$

Short Answer

Expert verified

Part (a). $\sqrt{21 p} = {(21)}^{\frac{1}{2}}$

Part (b). $\sqrt[4]{8 q} = {(8 q)}^{\frac{1}{4}}$

Part (c). $4 \sqrt[6]{36 r} = 4 {(36 r)}^{\frac{1}{6}}$

Step by step solution

Part (a) Step 1. Rational exponent of 21p

We know that, $\sqrt[n]{a} = a^{\frac{1}{n}}$

The index is $2$

The denominator of the exponent will be $2$ .

role="math" localid="1644757867840" $\sqrt{21 p} = {(21)}^{\frac{1}{2}}$

Part (b) Step 1. Rational exponent of 8q4

We know that, $\sqrt[n]{a} = a^{\frac{1}{n}}$

The index is $4$

The denominator of the exponent will be $4$ .

role="math" localid="1644757850228" $\sqrt[4]{8 q} = {(8 q)}^{\frac{1}{4}}$

Part (c) Step 1. Rational exponent of 436r6

We know that, $\sqrt[n]{a} = a^{\frac{1}{n}}$

The index is $6$

The denominator of the exponent will be $6$

role="math" localid="1644757919525" $4 \sqrt[6]{36 r} = 4 {(36 r)}^{\frac{1}{6}}$

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In the following exercises, write with a rational exponent.
$ⓐ \sqrt{21 p} ⓑ \sqrt[4]{48 q} ⓒ 4 \sqrt[6]{36 r}$

Short Answer

Step by step solution

Part (a) Step 1. Rational exponent of 21p

Part (b) Step 1. Rational exponent of 8q4

Part (c) Step 1. Rational exponent of 436r6

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In the following exercises, write with a rational exponent.ⓐ21pⓑ48q4ⓒ436r6

Short Answer

Step by step solution

Part (a) Step 1. Rational exponent of 21p

Part (b) Step 1. Rational exponent of 8q4

Part (c) Step 1. Rational exponent of 436r6

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Logic and Functions

Decision Maths

Applied Mathematics

Theoretical and Mathematical Physics

Calculus

Study anywhere. Anytime. Across all devices.

In the following exercises, write with a rational exponent.
$ⓐ \sqrt{21 p} ⓑ \sqrt[4]{48 q} ⓒ 4 \sqrt[6]{36 r}$