College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter R - Review Exercises: 47

Answer

$-\dfrac{12}{5}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the order of operations (PEMDAS - Parenthesis/Exponents, Multiplication/Division, Addition/Subtraction) to simplify the given expression, $ \dfrac{6(-4)-3^2(-2)^3}{-5[-2-(-6)]} .$ $\bf{\text{Solution Details:}}$ Simplifying the exponents, the expression above becomes \begin{array}{l}\require{cancel} \dfrac{6(-4)-9(-8)}{-5[-2-(-6)]} .\end{array} Simplifying the parenthesis, the expression above becomes \begin{array}{l}\require{cancel} \dfrac{6(-4)-9(-8)}{-5[-2+6]} \\\\= \dfrac{6(-4)-9(-8)}{-5[4]} .\end{array} Simplifying the product/quotient, the expression above becomes \begin{array}{l}\require{cancel} \dfrac{-24+72}{-20} .\end{array} Simplifying the sum/difference by making the fractions similar, the expression above becomes \begin{array}{l}\require{cancel} \dfrac{48}{-20} \\\\= \dfrac{\cancel4(12)}{\cancel4(-5)} \\\\= \dfrac{12}{-5} \\\\= -\dfrac{12}{5} .\end{array}
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