Evaluate ((z^2)/(5^4))^4

${(\frac{z^{2}}{5^{4}})}^{4}$

Step 1

Raise $5$ to the power of $4$ .

${(\frac{z^{2}}{625})}^{4}$

Step 2

Apply the product rule to $\frac{z^{2}}{625}$ .

$\frac{{(z^{2})}^{4}}{625^{4}}$

Step 3

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

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

$\frac{z^{2 \cdot 4}}{625^{4}}$

Multiply $2$ by $4$ .

$\frac{z^{8}}{625^{4}}$

Step 4

Raise $625$ to the power of $4$ .

$\frac{z^{8}}{152587890625}$