Solve frac{-(-x^{2})^{3}*(-y^2z)^3}{-(-xyz)^2*(-2xy)^0}

$$\frac { - ( - x ^ { 2 } ) ^ { 3 } \times ( - y ^ { 2 } z ) ^ { 3 } } { - ( - x y z ) ^ { 2 } \times ( - 2 x y ) ^ { 0 } }$$

Evaluate

$$z\left(xy\right)^{4}$$

Short Solution Steps

Expand \left(\left(-y^{2}\right)z\right)^{3}.

$$\frac{\left(-\left(-x^{2}\right)^{3}\right)\left(-y^{2}\right)^{3}z^{3}}{\left(-\left(\left(-x\right)yz\right)^{2}\right)\left(-2xy\right)^{0}}$$

Expand \left(\left(-x\right)yz\right)^{2}.

$$\frac{\left(-\left(-x^{2}\right)^{3}\right)\left(-y^{2}\right)^{3}z^{3}}{\left(-\left(-x\right)^{2}y^{2}z^{2}\right)\left(-2xy\right)^{0}}$$

Calculate -x to the power of 2 and get x^{2}.

$$\frac{\left(-\left(-x^{2}\right)^{3}\right)\left(-y^{2}\right)^{3}z^{3}}{\left(-x^{2}y^{2}z^{2}\right)\left(-2xy\right)^{0}}$$

Calculate -2xy to the power of 0 and get 1.

$$\frac{\left(-\left(-x^{2}\right)^{3}\right)\left(-y^{2}\right)^{3}z^{3}}{\left(-x^{2}y^{2}z^{2}\right)\times 1}$$

Factor the expressions that are not already factored.

$$\frac{-z^{3}\left(-x^{2}\right)^{3}\left(-y^{2}\right)^{3}}{-x^{2}y^{2}z^{2}}$$

Cancel out -z^{2} in both numerator and denominator.

$$\frac{z\left(-x^{2}\right)^{3}\left(-y^{2}\right)^{3}}{x^{2}y^{2}}$$

Expand the expression.

$$\frac{z\left(xy\right)^{6}}{\left(xy\right)^{2}}$$

Cancel out \left(xy\right)^{2} in both numerator and denominator.

$$z\left(xy\right)^{4}$$

Expand \left(xy\right)^{4}.

$$zx^{4}y^{4}$$

Differentiate w.r.t. x

$$4zx^{3}y^{4}$$