Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 1 - Section 1.3 - Exponents, Order of Operations, and Variable Expressions - Exercise Set: 47

Answer

$\Big(\dfrac{2}{3}\Big)^{3}+\dfrac{1}{9}+\dfrac{1}{3}\cdot\dfrac{4}{3}=\dfrac{23}{27}$

Work Step by Step

$\Big(\dfrac{2}{3}\Big)^{3}+\dfrac{1}{9}+\dfrac{1}{3}\cdot\dfrac{4}{3}$ First, evaluate the exponential expression: $\Big(\dfrac{2}{3}\Big)^{3}+\dfrac{1}{9}+\dfrac{1}{3}\cdot\dfrac{4}{3}=\dfrac{8}{27}+\dfrac{1}{9}+\dfrac{1}{3}\cdot\dfrac{4}{3}=...$ Now, evaluate the product: $...=\dfrac{8}{27}+\dfrac{1}{9}+\dfrac{4}{9}=...$ Finally, evaluate the sums and simplify if possible: $...=\dfrac{8}{27}+\dfrac{5}{9}=\dfrac{(8)(9)+(27)(5)}{(27)(9)}=...$ $...=\dfrac{72+135}{243}=\dfrac{207}{243}=\dfrac{23}{27}$
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