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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: Q9.229. (page 1139)

Simplify: a) $\frac{u^{\frac{5}{4}}}{u^{\frac{1}{4}}}$ b) $\frac{y^{\frac{3}{5}}}{y^{\frac{2}{5}}}$ c) $\frac{x^{\frac{2}{3}}}{x^{\frac{5}{3}}} .$

Short Answer

Expert verified

Part a) $\frac{u^{\frac{5}{4}}}{u^{\frac{1}{4}}} = u .$

Part b) $\frac{y^{\frac{3}{5}}}{y^{\frac{2}{5}}} = y^{\frac{1}{5}} .$

Part c) $\frac{x^{\frac{2}{3}}}{x^{\frac{5}{3}}} = \frac{1}{x} .$

Step by step solution

01

Part (a) Step 1 : Given Information

The given expression is $\frac{u^{\frac{5}{4}}}{u^{\frac{1}{4}}} .$

02

Part (a) Step 2: Simplification

$\frac{u^{\frac{5}{4}}}{u^{\frac{1}{4}}} = u^{\frac{5}{4} - \frac{1}{4}} = u^{\frac{5 - 1}{4}} = u^{\frac{4}{4}} = u H e n c e, \frac{u^{\frac{5}{4}}}{u^{\frac{1}{4}}} = u .$

03

Part (b) Step 1: Given information

The given expression is $\frac{y^{\frac{3}{5}}}{y^{\frac{2}{5}}} .$

04

Part (b) Step 2: Simplification

Using the formula $\frac{a^{m}}{a^{n}} = a^{m - n} .$

$\frac{y^{\frac{3}{5}}}{y^{\frac{2}{5}}} = y^{\frac{3}{5} - \frac{2}{5}} = y^{\frac{3 - 2}{5}} = y^{\frac{1}{5}} = \sqrt[5]{y} H e n c e, \frac{y^{\frac{3}{5}}}{y^{\frac{2}{5}}} = \sqrt[5]{y} .$

05

Part (c) Step 1: Given information

The given expression is $\frac{x^{\frac{2}{3}}}{x^{\frac{5}{3}}} .$

06

Part (c) Step 2: Simplification

$\frac{x^{\frac{2}{3}}}{x^{\frac{5}{3}}} = x^{\frac{2}{3} - \frac{5}{3}} = x^{\frac{2 - 5}{3}} = x^{\frac{- 3}{3}} = \frac{1}{x} H e n c e, \frac{x^{\frac{2}{3}}}{x^{\frac{5}{3}}} = \frac{1}{x} .$

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Most popular questions from this chapter

In the following exercises, solve.

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