Algebra: A Combined Approach (4th Edition)

Published by Pearson

Chapter 1 - Section 1.3 - Exponents, Order of Operations, and Variable Expressions - Exercise Set - Page 28: 48

Answer

$\Big(\dfrac{3}{8}\Big)^{2}+\dfrac{1}{4}+\dfrac{1}{8}\cdot\dfrac{3}{2}=\dfrac{37}{64}$

Work Step by Step

$\Big(\dfrac{3}{8}\Big)^{2}+\dfrac{1}{4}+\dfrac{1}{8}\cdot\dfrac{3}{2}$ First, evaluate the exponential expression: $\Big(\dfrac{3}{8}\Big)^{2}+\dfrac{1}{4}+\dfrac{1}{8}\cdot\dfrac{3}{2}=\dfrac{9}{64}+\dfrac{1}{4}+\dfrac{1}{8}\cdot\dfrac{3}{2}=...$ Now, evaluate the product: $...=\dfrac{9}{64}+\dfrac{1}{4}+\dfrac{3}{16}=...$ Finally, evaluate the sums: $...=\dfrac{36+64}{256}+\dfrac{3}{16}=\dfrac{100}{256}+\dfrac{3}{16}=\dfrac{25}{64}+\dfrac{3}{16}=...$ $...=\dfrac{400+192}{1024}=\dfrac{592}{1024}=\dfrac{37}{64}$

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