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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 483 (page 1125)

Use the Quotient Property to Simplify Expressions with Higher Roots
a) $\frac{\sqrt[3]{- 625}}{\sqrt[3]{5}}$
b) $\frac{\sqrt[4]{80 m^{7}}}{\sqrt[4]{5 m}}$

Short Answer

Expert verified

Part (a) $\frac{\sqrt[3]{- 625}}{\sqrt[3]{5}} = - 5$

Part (b) $\frac{\sqrt[4]{80 m^{7}}}{\sqrt[4]{5 m}} = 2 m \sqrt[4]{m^{2}}$

Step by step solution

01

Part (a)Step 1:Given information

The given expression is $\frac{\sqrt[3]{- 625}}{\sqrt[3]{5}}$

02

Part (a)Step 2:Simplification

Simplify the fraction under the radical first. $\sqrt[3]{\frac{- 625}{5}}$

$= \sqrt[3]{- 125}$

Simplify $\sqrt[3]{{(- 5)}^{3}}$

$- 5$

03

Part (b)Step 1:Given information

The given expression is $\frac{\sqrt[4]{80 m^{7}}}{\sqrt[4]{5 m}}$

04

Part (b)Step 2:Simplification

Simplify the fraction under the radical first. $\sqrt[4]{\frac{80 m^{7}}{5 m}}$

$= \sqrt[4]{16 m^{6}}$

Rewrite the radicand using perfect fourth power factors. $\sqrt[4]{2^{4} m^{4} . m^{2}}$

Simplify $2 m \sqrt[4]{m^{2}}$

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Most popular questions from this chapter

Accident investigation: An accident investigator measured the skid marks of one of the vehicles involved in an accident. The length of the skid marks was 175 feet. Use the formula $s = \sqrt{24 d}$ to find the speed of the vehicle before the brakes were applied. Round your answer to the nearest tenth.

Try It.

Sergio wants to make a square mosaic as an inlay for a table he is building. He has enough tile to cover an area of $2704$ square centimeters. Use the formula $s = \sqrt{A}$ to find the length of each side of his mosaic. Round your answer to the nearest tenth of a centimeter.

In the following exercises, simplify.

$\frac{\sqrt{26 y^{7}}}{\sqrt{2 y}}$

In the following exercises, solve:

(a) $\sqrt{a} + 2 = \sqrt{a + 4}$

(b) $\sqrt{b - 2} + 1 = \sqrt{3 b + 2}$ .

Solve: $\sqrt{3 m + 2} - 5 = 0$

See all solutions

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