Simplify the Radical Expression ((z^4)/(6^2))^-3

${(\frac{z^{4}}{6^{2}})}^{- 3}$

Step 1

Raise $6$ to the power of $2$ .

${(\frac{z^{4}}{36})}^{- 3}$

Step 2

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{36}{z^{4}})}^{3}$

Step 3

Apply the product rule to $\frac{36}{z^{4}}$ .

$\frac{36^{3}}{{(z^{4})}^{3}}$

Step 4

Raise $36$ to the power of $3$ .

$\frac{46656}{{(z^{4})}^{3}}$

Step 5

Multiply the exponents in ${(z^{4})}^{3}$ .

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

$\frac{46656}{z^{4 \cdot 3}}$

Multiply $4$ by $3$ .

$\frac{46656}{z^{12}}$