Answer
$17,920$
Work Step by Step
(See p. 884)
The term that contains $a^{r}$
in the expansion of $(a+b)^{n}$ is$ \left(\begin{array}{l}
n\\
r
\end{array}\right)a^{r}b^{n-r}$.
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We are searching for the term $\displaystyle \left(\begin{array}{l}
8\\
r
\end{array}\right)(8x)^{r}(\frac{1}{2x})^{8-r}$
in which the exponent of x is zero:
$\displaystyle \frac{x^{r}}{x^{8-r}}=x^{0}$
$x^{r}=x^{8-r}$
$r=8-r$
$2r=8$
$r=4$
So the term is
$\displaystyle \left(\begin{array}{l}
8\\
4
\end{array}\right)(8x)^{4}(\frac{1}{2x})^{8-4}=\frac{8\cdot 7\cdot 6\cdot 5}{1\cdot 2\cdot 3\cdot 4}\cdot\frac{8^{4}}{2^{4}}\cdot x^{0}$
$=70\displaystyle \cdot(\frac{8}{2})^{4}=70\cdot 4^{4}=17,920$
