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

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

Step 1

Move the negative in front of the fraction.

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

Step 2

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

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

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

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

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

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

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

Step 3

Simplify the expression.

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

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

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

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

Step 4

Simplify the numerator.

Raise $3$ to the power of $2$ .

$\frac{9 {(w^{3})}^{2}}{v^{2}}$

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

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

$\frac{9 w^{3 \cdot 2}}{v^{2}}$

Multiply $3$ by $2$ .

$\frac{9 w^{6}}{v^{2}}$