Chapter 8: Q. 8.54 (page 776)

Write with a rational exponent:
(a) $\sqrt[7]{3 k}$
(b) $\sqrt[4]{5 j}$
(c) $8 \sqrt[3]{2 a}$

Short Answer

Expert verified

The rational exponent of $\sqrt[7]{3 k}$ is ${(3 k)}^{\frac{1}{7}}$

The rational exponent of $\sqrt[4]{5 j}$ is ${(5 j)}^{\frac{1}{4}}$

The rational exponent of $8 \sqrt[3]{2 a}$ is $8 {(2 a)}^{\frac{1}{3}}$

Step by step solution

Part (a) Given

The radical expression $\sqrt[7]{3 k}$

To write each radical in the form of $a^{\frac{1}{n}}$

Part (a) Step 2. Write as rational exponent

The index is $7$ , so the denominator of the exponent will be $7$ .

Put parentheses around the entire expression.

The rational exponent is ${(3 k)}^{\frac{1}{7}}$

Part (b) Step 1. Given

The radical expression is $\sqrt[4]{5 j}$

To write each radical in the form of $a^{\frac{1}{n}}$

Part (b) Step 2. Write as rational exponent

The index is $4$ , so the denominator of the exponent will be $4$

Put parentheses around the entire expression.

The rational exponent is ${(5 j)}^{\frac{1}{4}}$

Part (c) Step 1. Given

The radical expression is $8 \sqrt[3]{2 a}$

To write each radical in the form of $a^{\frac{1}{n}}$

Part (c) Step 2. Write as rational exponent

The index is $3$ , so the denominator of the exponent will be $3$

Put parentheses around the entire expression.

The rational exponent is $8 {(2 a)}^{\frac{1}{3}}$

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Write with a rational exponent:
(a) $\sqrt[7]{3 k}$
(b) $\sqrt[4]{5 j}$
(c) $8 \sqrt[3]{2 a}$

Short Answer

Step by step solution

Part (a) Given

Part (a) Step 2. Write as rational exponent

Part (b) Step 1. Given

Part (b) Step 2. Write as rational exponent

Part (c) Step 1. Given

Part (c) Step 2. Write as rational exponent

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Write with a rational exponent:(a) 3k7(b) 5j4(c) 82a3

Short Answer

Step by step solution

Part (a) Given

Part (a) Step 2. Write as rational exponent

Part (b) Step 1. Given

Part (b) Step 2. Write as rational exponent

Part (c) Step 1. Given

Part (c) Step 2. Write as rational exponent

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

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Study anywhere. Anytime. Across all devices.

Write with a rational exponent:
(a) $\sqrt[7]{3 k}$
(b) $\sqrt[4]{5 j}$
(c) $8 \sqrt[3]{2 a}$