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: 36



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{4(-2-3)^2}{5}-\dfrac{5(-1-5)^2}{6} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{4(-5)^2}{5}-\dfrac{5(-6)^2}{6} \\\\= \dfrac{4(-5)(-5)}{5}-\dfrac{5(-6)(-6)}{6} \\\\= \dfrac{4(-\cancel{5})(-5)}{\cancel{5}}-\dfrac{5(-\cancel{6})(-6)}{\cancel{6}} \\\\= 20-30 \\\\= -10 .\end{array}
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