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

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

Step 1

Move $w^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(v w^{2})}^{- 3}$

Step 2

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

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

Step 3

Simplify the denominator.

Apply the product rule to $v w^{2}$ .

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

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

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

$\frac{1}{v^{3} w^{2 \cdot 3}}$

Multiply $2$ by $3$ .

$\frac{1}{v^{3} w^{6}}$