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:
$...=\dfrac{36+64}{256}+\dfrac{3}{16}=\dfrac{100}{256}+\dfrac{3}{16}=\dfrac{25}{64}+\dfrac{3}{16}=...$
$...=\dfrac{400+192}{1024}=\dfrac{592}{1024}=\dfrac{37}{64}$