Simplify ((-12x^3y^4)/(4x^3y^4))^2

${(\frac{- 12 x^{3} y^{4}}{4 x^{3} y^{4}})}^{2}$

Cancel the common factor of $- 12$ and $4$ .

Factor $4$ out of $- 12 x^{3} y^{4}$ .

${(\frac{4 (- 3 x^{3} y^{4})}{4 x^{3} y^{4}})}^{2}$

Cancel the common factors.

Factor $4$ out of $4 x^{3} y^{4}$ .

${(\frac{4 (- 3 x^{3} y^{4})}{4 (x^{3} y^{4})})}^{2}$

Cancel the common factor.

${(\frac{4 (- 3 x^{3} y^{4})}{4 (x^{3} y^{4})})}^{2}$

Rewrite the expression.

${(\frac{- 3 x^{3} y^{4}}{x^{3} y^{4}})}^{2}$

Cancel the common factor of $x^{3}$ .

Cancel the common factor.

${(\frac{- 3 x^{3} y^{4}}{x^{3} y^{4}})}^{2}$

Rewrite the expression.

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

Cancel the common factor of $y^{4}$ .

Cancel the common factor.

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

Divide $- 3$ by $1$ .

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

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

$9$