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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 589. (page 1145)

Simplify:
(a) $\frac{m^{\frac{7}{4}} m^{\frac{- 5}{4}}}{m^{\frac{- 2}{4}}}$
(b) $\frac{n^{\frac{3}{7}} n}{n^{\frac{- 4}{7}}}$

Short Answer

Expert verified

(a) $\frac{m^{\frac{7}{4}} m^{\frac{- 5}{4}}}{m^{\frac{- 2}{4}}} = m$

(b)localid="1651166347402" $\frac{n^{\frac{3}{7}} n}{n^{\frac{- 4}{7}}} = n^{2}$

Step by step solution

01

Part (a) Step 1: Given Information

The given expression is $\frac{m^{\frac{7}{4}} m^{\frac{- 5}{4}}}{m^{\frac{- 2}{4}}}$

02

Part (a) Step 2: Simplification

$\frac{m^{\frac{7}{4}} m^{\frac{- 5}{4}}}{m^{\frac{- 2}{4}}}$

Use product property in numerator, add the exponents

$= \frac{m^{\frac{7 - 5}{4}}}{m^{\frac{- 2}{4}}}$

$= \frac{m^{\frac{2}{4}}}{m^{\frac{- 2}{4}}}$

Use the quotient property, subtract the exponents

localid="1651166048592" $= m^{\frac{2}{4} + \frac{2}{4}}$

$= m^{\frac{4}{4}}$

$= m$

03

Part (b) Step 1: Given Information

The given expression is $\frac{n^{\frac{3}{7}} n}{n^{\frac{- 4}{7}}}$

04

Part (b) Step 2: Simplification

$\frac{n^{\frac{3}{7}} n}{n^{\frac{- 4}{7}}}$

Use product property in numerator, add the exponents

$= \frac{n^{\frac{3}{7} + 1}}{n^{\frac{- 4}{7}}}$

$= \frac{n^{\frac{3 + 7}{7}}}{n^{\frac{- 4}{7}}}$

$= \frac{n^{\frac{10}{7}}}{n^{\frac{- 4}{7}}}$

Use the quotient property, subtract the exponents

$= n^{\frac{10 + 4}{7}}$

$= n^{\frac{14}{7}}$

$= n^{2}$

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