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: 34

Answer

$-1$

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}{16}-\dfrac{2(3)^2}{6} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{4(2)(2)(2)}{16}-\dfrac{2(3)(3)}{6} \\\\= \dfrac{\cancel{2}\cdot2(\cancel{2})(\cancel{2})(\cancel{2})}{\cancel{2}(\cancel{2})(\cancel{2})(\cancel{2})}-\dfrac{\cancel{2}(3)(\cancel{3})}{\cancel{2}(\cancel{3})} \\\\= 2-3 \\\\= -1 .\end{array}
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