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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 587. (page 1145)

Simplify:
(a) $\frac{a^{\frac{3}{4}} a^{\frac{- 1}{4}}}{a^{\frac{- 10}{4}}}$
(b) $\frac{b^{\frac{2}{3}} b}{b^{\frac{- 7}{3}}}$

Short Answer

Expert verified

(a) $\frac{a^{\frac{3}{4}} a^{\frac{- 1}{4}}}{a^{\frac{- 10}{4}}} = a^{3}$

(b)role="math" localid="1651163763777" $\frac{b^{\frac{2}{3}} b}{b^{\frac{- 7}{3}}} = b^{4}$

Step by step solution

01

Part (a) Step 1: Given Information

The given expression is $\frac{a^{\frac{3}{4}} a^{\frac{- 1}{4}}}{a^{\frac{- 10}{4}}}$

02

Part (a) Step 2: Simplification

$\frac{a^{\frac{3}{4}} a^{\frac{- 1}{4}}}{a^{\frac{- 10}{4}}}$

Use product property in numerator, add the exponents

$= \frac{a^{\frac{3}{4} - \frac{1}{4}}}{a^{\frac{- 10}{4}}}$

$= \frac{a^{\frac{2}{4}}}{a^{\frac{- 10}{4}}}$

Use the quotient property, subtract the exponents

$= a^{\frac{2}{4} + \frac{10}{4}}$

$= a^{\frac{12}{4}}$

$= a^{3}$

03

Part (b) Step 1: Given Information

The given expression is $\frac{b^{\frac{2}{3}} b}{b^{\frac{- 7}{3}}}$

04

Part (b) Step 2: Simplification

$\frac{b^{\frac{2}{3}} b}{b^{\frac{- 7}{3}}}$

Use product property in numerator, add the exponents

$= \frac{b^{\frac{2}{3} + 1}}{b^{\frac{- 7}{3}}}$

$= \frac{b^{\frac{2 + 3}{3}}}{b^{\frac{- 7}{3}}}$

$= \frac{b^{\frac{5}{3}}}{b^{\frac{- 7}{3}}}$

Use the quotient property, subtract the exponents

$= b^{\frac{5}{3} + \frac{7}{3}}$

$= b^{\frac{12}{3}}$

$= b^{4}$

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