Simplify (1/4a^8b^4)^2

${(\frac{1}{4} a^{8} b^{4})}^{2}$

Multiply $\frac{1}{4} (a^{8} b^{4})$ .

Combine $a^{8}$ and $\frac{1}{4}$ .

${(\frac{a^{8}}{4} b^{4})}^{2}$

Combine $\frac{a^{8}}{4}$ and $b^{4}$ .

${(\frac{a^{8} b^{4}}{4})}^{2}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $\frac{a^{8} b^{4}}{4}$ .

$\frac{{(a^{8} b^{4})}^{2}}{4^{2}}$

Apply the product rule to $a^{8} b^{4}$ .

$\frac{{(a^{8})}^{2} {(b^{4})}^{2}}{4^{2}}$

Simplify the numerator.

Multiply the exponents in ${(a^{8})}^{2}$ .

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

$\frac{a^{8 \cdot 2} {(b^{4})}^{2}}{4^{2}}$

Multiply $8$ by $2$ .

$\frac{a^{16} {(b^{4})}^{2}}{4^{2}}$

Multiply the exponents in ${(b^{4})}^{2}$ .

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

$\frac{a^{16} b^{4 \cdot 2}}{4^{2}}$

Multiply $4$ by $2$ .

$\frac{a^{16} b^{8}}{4^{2}}$

Raise $4$ to the power of $2$ .

$\frac{a^{16} b^{8}}{16}$