Simplify (-(w^3)/6)^-2

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

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

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

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

Apply the product rule to $- \frac{6}{w^{3}}$ .

${(- 1)}^{2} {(\frac{6}{w^{3}})}^{2}$

Apply the product rule to $\frac{6}{w^{3}}$ .

${(- 1)}^{2} \frac{6^{2}}{{(w^{3})}^{2}}$

Raise $- 1$ to the power of $2$ .

$1 \frac{6^{2}}{{(w^{3})}^{2}}$

Multiply $\frac{6^{2}}{{(w^{3})}^{2}}$ by $1$ .

$\frac{6^{2}}{{(w^{3})}^{2}}$

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

$\frac{36}{{(w^{3})}^{2}}$

Multiply the exponents in ${(w^{3})}^{2}$ .

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

$\frac{36}{w^{3 \cdot 2}}$

Multiply $3$ by $2$ .

$\frac{36}{w^{6}}$