Chapter 8: Q. 8.59 (page 778)

Write with a rational exponent:
(a) $\sqrt{x^{5}}$
(b) ${(\sqrt[4]{3 y})}^{3}$
(c) $\sqrt{{(\frac{2 m}{3 n})}^{5}}$

Short Answer

Expert verified

The rational exponent of $\sqrt{x^{5}}$ is $x^{\frac{5}{2}}$

The rational exponent of ${(\sqrt[4]{3 y})}^{3}$ is ${(3 y)}^{\frac{3}{4}}$

The rational exponent of $\sqrt{{(\frac{2 m}{3 n})}^{5}}$ is ${(\frac{2 m}{3 n})}^{\frac{5}{2}}$

Step by step solution

Part (a) Step 1. Given

The radical expression $\sqrt{x^{5}}$

To write the expression with a rational exponent.

Part (a) Step 2. Find numerator and denominator of exponent from the given expression

The numerator of the exponent is exponent, $5$ .

The denominator of the exponent is the index of the radical, $2$ .

So the rational exponent is ${(x)}^{\frac{5}{2}}$

Part (b) Step 1. Given

The radical expression ${(\sqrt[4]{3 y})}^{3}$

To write the expression with a rational exponent.

Part (b) Step 2. Find numerator and denominator of exponent from the given expression

The numerator of the exponent is exponent, $3$ .

The denominator of the exponent is the index of the radical, $4$ .

So the rational exponent is ${(3 y)}^{\frac{3}{4}}$

Part (c) Step 1. Given

The radical expression $\sqrt{{(\frac{2 m}{3 n})}^{5}}$

To write the expression with a rational exponent.

Part (c) Step 2. Find numerator and denominator of exponent from the given expression

The numerator of the exponent is exponent, $5$ .

The denominator of the exponent is the index of the radical, $2$ .

So the rational exponent is ${(\frac{2 m}{3 n})}^{\frac{5}{2}}$

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Write with a rational exponent:
(a) $\sqrt{x^{5}}$
(b) ${(\sqrt[4]{3 y})}^{3}$
(c) $\sqrt{{(\frac{2 m}{3 n})}^{5}}$

Short Answer

Step by step solution

Part (a) Step 1. Given

Part (a) Step 2. Find numerator and denominator of exponent from the given expression

Part (b) Step 1. Given

Part (b) Step 2. Find numerator and denominator of exponent from the given expression

Part (c) Step 1. Given

Part (c) Step 2. Find numerator and denominator of exponent from the given expression

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Write with a rational exponent:(a)x5(b)(3y4)3(c) (2m3n)5

Short Answer

Step by step solution

Part (a) Step 1. Given

Part (a) Step 2. Find numerator and denominator of exponent from the given expression

Part (b) Step 1. Given

Part (b) Step 2. Find numerator and denominator of exponent from the given expression

Part (c) Step 1. Given

Part (c) Step 2. Find numerator and denominator of exponent from the given expression

One App. One Place for Learning.

Most popular questions from this chapter

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Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Write with a rational exponent:
(a) $\sqrt{x^{5}}$
(b) ${(\sqrt[4]{3 y})}^{3}$
(c) $\sqrt{{(\frac{2 m}{3 n})}^{5}}$