Chapter 8: Q. 125 (page 786)

In the following exercises, write with a rational exponent.
$\sqrt[3]{7 c} ⓑ \sqrt[7]{12 d} ⓒ 2 \sqrt[4]{6 b}$

Short Answer

Expert verified

Part (a). $\sqrt[3]{7 c} = {(7 c)}^{\frac{1}{3}}$

Part (b). $\sqrt[7]{12 d} = {(12 d)}^{\frac{1}{7}}$

Part (c). $2 \sqrt[4]{6 b} = 2 {(6 b)}^{\frac{1}{4}}$

Step by step solution

Part (a) Step 1. Rational exponent of 73

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

The index is $3$

The denominator of the exponent will be $3$ .

$\sqrt[3]{7 c} = {(7 c)}^{\frac{1}{3}}$

Part (b) Step 1. Rational exponent of 12d7

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

The index is $7$

The denominator of the exponent will be $7$

$\sqrt[7]{12 d} = {(12 d)}^{\frac{1}{7}}$

Part (c) Step 1. Rational exponent of 26b5

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

The index is $5$

The denominator of the exponent will be $5$ .

$2 \sqrt[4]{6 b} = 2 {(6 b)}^{\frac{1}{4}}$

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In the following exercises, write with a rational exponent.
$\sqrt[3]{7 c} ⓑ \sqrt[7]{12 d} ⓒ 2 \sqrt[4]{6 b}$

Short Answer

Step by step solution

Part (a) Step 1. Rational exponent of 73

Part (b) Step 1. Rational exponent of 12d7

Part (c) Step 1. Rational exponent of 26b5

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In the following exercises, write with a rational exponent. 7c3ⓑ12d7ⓒ26b4

Short Answer

Step by step solution

Part (a) Step 1. Rational exponent of 73

Part (b) Step 1. Rational exponent of 12d7

Part (c) Step 1. Rational exponent of 26b5

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Applied Mathematics

Theoretical and Mathematical Physics

Pure Maths

Calculus

Geometry

Study anywhere. Anytime. Across all devices.

In the following exercises, write with a rational exponent.
$\sqrt[3]{7 c} ⓑ \sqrt[7]{12 d} ⓒ 2 \sqrt[4]{6 b}$