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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 9: Q 534 (page 1143)

Simplify Expressions with $a^{\frac{1}{n}}$
Write with a rational exponent.
a) $\sqrt{21 p}$
b) $\sqrt[4]{8 q}$
c) $4 \sqrt[6]{36 r}$

Short Answer

Expert verified

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

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

01

Part (a) Step 1 : Given Information

The given expression is $\sqrt{21 p}$

02

Part (a) Step 2: Simplification

No index is shown, so it is 2. The denominator of the exponent will be 2.

$鈭� \sqrt{21 p} = {(21 p)}^{\frac{1}{2}}$

03

Part (b) Step 1: Given information

The given expression is $\sqrt[4]{8 q}$

04

Part (b) Step 2: Simplification

The index is 4, so the denominator of the exponent is 4.

$鈭� \sqrt[4]{8 q} = {(8 q)}^{\frac{1}{4}}$

05

Part (c) Step 1: Given information

The given expression is $4 \sqrt[6]{36 r}$

06

Part (c) Step 2: Simplification

The index is 6, so the denominator of the exponent is 6.

$鈭� 4 \sqrt[6]{36 r} = 4 {(36 r)}^{\frac{1}{6}}$

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