Find the Product (a^-2*8^7)^2

${(a^{- 2} \cdot 8^{7})}^{2}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{1}{a^{2}} \cdot 8^{7})}^{2}$

Raise $8$ to the power of $7$ .

${(\frac{1}{a^{2}} \cdot 2097152)}^{2}$

Combine $\frac{1}{a^{2}}$ and $2097152$ .

${(\frac{2097152}{a^{2}})}^{2}$

Simplify the expression.

Apply the product rule to $\frac{2097152}{a^{2}}$ .

$\frac{2097152^{2}}{{(a^{2})}^{2}}$

Raise $2097152$ to the power of $2$ .

$\frac{4398046511104}{{(a^{2})}^{2}}$

Multiply the exponents in ${(a^{2})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{4398046511104}{a^{2 \cdot 2}}$

Multiply $2$ by $2$ .

$\frac{4398046511104}{a^{4}}$