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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 9.234. (page 1142)

Simplify:
a) $\frac{u^{\frac{4}{5}} . u^{\frac{- 2}{5}}}{u^{\frac{- 13}{5}}}$
b) $\frac{v^{\frac{1}{2}} . v}{v^{\frac{- 7}{2}}}$

Short Answer

Expert verified

a) $\frac{u^{\frac{4}{5}} . u^{\frac{- 2}{5}}}{u^{\frac{- 13}{5}}} = u^{3}$

b) $\frac{v^{\frac{1}{2}} . v}{v^{\frac{- 7}{2}}} = v^{5}$

Step by step solution

01

Part (a) Step 1: Given Information

The given expression is $\frac{u^{\frac{4}{5}} . u^{\frac{- 2}{5}}}{u^{\frac{- 13}{5}}}$ .

02

Part (a) Step 2: Simplification

$\frac{u^{\frac{4}{5}} . u^{\frac{- 2}{5}}}{u^{\frac{- 13}{5}}}$

Use product property in numerator and add the exponents.

$= \frac{u^{\frac{4 - 2}{5}}}{u^{\frac{- 13}{5}}}$

$= \frac{u^{\frac{2}{5}}}{u^{\frac{- 13}{5}}}$

Use quotient property and subtract the exponents

$= u^{\frac{2 + 13}{5}}$

$= u^{\frac{15}{5}}$

$= u^{3}$

03

Part (b) Step 1: Given Information

The given expression is $\frac{v^{\frac{1}{2}} . v}{v^{\frac{- 7}{2}}}$ .

04

Part (b) Step 2: Simplification

$\frac{v^{\frac{1}{2}} . v}{v^{\frac{- 7}{2}}}$

Use product property in numerator and add the exponents

role="math" localid="1650395207416" $= \frac{v^{\frac{1}{2} + 1}}{v^{\frac{- 7}{2}}}$

$= \frac{v^{\frac{3}{2}}}{v^{\frac{- 7}{2}}}$

Use quotient property and subtract the exponents

$= v^{\frac{3 + 7}{2}}$

$= v^{\frac{10}{2}}$

$= v^{5}$

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