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: 40

Answer

$-\dfrac{7}{9}$

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{-3-2[(3-5)^2-2]}{(-2-1)^2} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{-3-2[(-2)^2-2]}{(-3)^2} \\\\= \dfrac{-3-2[(-2)(-2)-2]}{(-3)(-3)} \\\\= \dfrac{-3-2[4-2]}{9} \\\\= \dfrac{-3-2[2]}{9} \\\\= \dfrac{-3-4}{9} \\\\= \dfrac{-7}{9} \\\\= -\dfrac{7}{9} .\end{array}
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