Elementary Algebra

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

Chapter 2 - Real Numbers - 2.4 - Exponents - Problem Set 2.4 - Page 75: 37



Work Step by Step

Recall, in order to solve problems involving order of operations, we use the PEMDAS rule. First Priority: P - parentheses and other grouping symbols (including fraction bars) Second Priority: E - exponents Third Priority: M/D - Multiplication or division, whichever comes first from the left to the right Fourth Priority: A/S - Addition or subtraction, whichever comes first from the left to the right We follow order of operations to obtain that the expression, $ \dfrac{-5(2-3)^3}{2}-\dfrac{4(2-4)^3}{3} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{-5(-1)^3}{2}-\dfrac{4(-2)^3}{3} \\\\= \dfrac{-5(-1)(-1)(-1)}{2}-\dfrac{4(-2)(-2)(-2)}{3} \\\\= \dfrac{5}{2}-\dfrac{-32}{3} \\\\= \dfrac{15}{6}+\dfrac{64}{6} \\\\= \dfrac{79}{6} .\end{array}
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