Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 4 - Proportions, Percents, and Solving Inequalities - Chapters 1-4 Cumulative Review Problem Set: 26

Answer

$-\frac{1}{512}$

Work Step by Step

First, we will simplify the expression within the parenthesis by finding the least common denominator: $(\frac{3}{4}-\frac{7}{8})^{3}$ =$(\frac{3(2)-1(7)}{8})^{3}$ =$(\frac{6-7}{8})^{3}$ =$(\frac{-1}{8})^{3}$ Next, we raise both the numerator and the denominator to the power of $3$ and simplify: $(\frac{-1}{8})^{3}=\frac{(-1)^{3}}{8^{3}}=\frac{-1\times-1\times-1}{8\times8\times8}=\frac{-1}{512}=-\frac{1}{512}$
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