Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 1 - Section 1.8 - Exponents and Order of Operations - Exercise Set - Page 100: 92

Answer

The expression we found was $[2(9 - 11)]^4$. The expression is evaluated to $256$.

Work Step by Step

First, we need to translate the different portions of this problem: Subtract $11$ from $9$: $$9 - 11$$ Multiply this difference by $2$: $$2(9 - 11)$$ Raise the product to the fourth power: $$[2(9 - 11)]^4$$ According to order of operations, represented by the acronym PEMDAS, we evaluate parentheses first (starting with inner parentheses), then exponents and radicals, then multiplication and division, and, finally, addition and subtraction. Therefore, we evaluate the parentheses first, starting with the innermost ones: $$[2(-2)]^4$$ We then evaluate the next level of brackets: $$(-4)^4$$ Finally, we evaluate the exponent: $$256$$ The expression is evaluated to $256$.
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