use the power - reduction formulas to rewrite the expression. (hint: your answer should not contain any…

Explanation:

Step1: Recall power - reduction formula

The power - reduction formula for $\sin^{2}\theta$ is $\sin^{2}\theta=\frac{1 - \cos(2\theta)}{2}$.

Step2: Substitute $\theta = 8x$

Let $\theta = 8x$. Then $\sin^{2}(8x)=\frac{1-\cos(2\times8x)}{2}=\frac{1 - \cos(16x)}{2}$.

Answer:

$\frac{1-\cos(16x)}{2}$