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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: Q9.230. (page 1139)

Simplify: a) $\frac{c^{\frac{12}{5}}}{c^{\frac{2}{5}}}$ b) $\frac{m^{\frac{5}{4}}}{m^{\frac{9}{4}}}$ c) $\frac{d^{\frac{1}{5}}}{d^{\frac{6}{5}}} .$

Short Answer

Expert verified

Part a) $\frac{c^{\frac{12}{5}}}{c^{\frac{2}{5}}} = c^{2}$

Part b) $\frac{m^{\frac{5}{4}}}{m^{\frac{9}{4}}} = \frac{1}{m}$

Part c) $\frac{d^{\frac{1}{5}}}{d^{\frac{6}{5}}} = \frac{1}{d} .$

Step by step solution

01

Part (a) Step 1 : Given Information

The given expression is $\frac{c^{\frac{12}{5}}}{c^{\frac{2}{5}}} .$

02

Part (a) Step 2: Simplification

$\frac{c^{\frac{12}{5}}}{c^{\frac{2}{5}}} = c^{\frac{12}{5} - \frac{2}{5}} = c^{\frac{12 - 2}{5}} = c^{2} H e n c e, \frac{c^{\frac{12}{5}}}{c^{\frac{2}{5}}} = c^{2} .$

03

Part (b) Step 1: Given information

The given expression is $\frac{m^{\frac{5}{4}}}{m^{\frac{9}{4}}} .$

04

Part (b) Step 2: Simplification

$\frac{m^{\frac{5}{4}}}{m^{\frac{9}{4}}} = m^{\frac{5}{4} - \frac{9}{4}} = m^{\frac{5 - 9}{4}} = m^{- 1} = \frac{1}{m} H e n c e, \frac{m^{\frac{5}{4}}}{m^{\frac{9}{4}}} = \frac{1}{m} .$

05

Part (c) Step 1: Given information

The given expression is $\frac{d^{\frac{1}{5}}}{d^{\frac{6}{5}}} .$

06

Part (c) Step 2: Simplification

$\frac{d^{\frac{1}{5}}}{d^{\frac{6}{5}}} = d^{\frac{1}{5} - \frac{6}{5}} = d^{- 1} = \frac{1}{d} H e n c e, \frac{d^{\frac{1}{5}}}{d^{\frac{6}{5}}} = \frac{1}{d} .$

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