Solve -left(-xy^3right)^2left(-xyright)^3/{left(-x^2right)^3{y}^10}

$$\frac{ - { \left(-x { y }^{ 3 } \right) }^{ 2 } { \left(-xy \right) }^{ 3 } }{ { \left(- { x }^{ 2 } \right) }^{ 3 } { y }^{ 10 } }$$

Evaluate

$$-\frac{1}{xy}$$

Short Solution Steps

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

$$\frac{\left(-\left(-x\right)^{2}\left(y^{3}\right)^{2}\right)\left(\left(-x\right)y\right)^{3}}{\left(-x^{2}\right)^{3}y^{10}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{\left(-\left(-x\right)^{2}y^{6}\right)\left(\left(-x\right)y\right)^{3}}{\left(-x^{2}\right)^{3}y^{10}}$$

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

$$\frac{\left(-x^{2}y^{6}\right)\left(\left(-x\right)y\right)^{3}}{\left(-x^{2}\right)^{3}y^{10}}$$

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

$$\frac{\left(-x^{2}y^{6}\right)\left(-x\right)^{3}y^{3}}{\left(-x^{2}\right)^{3}y^{10}}$$

Cancel out y^{3} in both numerator and denominator.

$$\frac{\left(-x\right)^{3}\left(-x^{2}y^{6}\right)}{\left(-x^{2}\right)^{3}y^{7}}$$

Factor the expressions that are not already factored.

$$\frac{-x^{2}\left(-x\right)^{3}y^{6}}{\left(-x^{2}\right)^{3}y^{7}}$$

Cancel out y^{6} in both numerator and denominator.

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

Expand the expression.

$$\frac{x^{5}}{-yx^{6}}$$

Cancel out x^{5} in both numerator and denominator.

$$\frac{1}{-xy}$$

Expand

$$-\frac{1}{xy}$$

Short Solution Steps

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

$$\frac{\left(-\left(-x\right)^{2}\left(y^{3}\right)^{2}\right)\left(\left(-x\right)y\right)^{3}}{\left(-x^{2}\right)^{3}y^{10}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{\left(-\left(-x\right)^{2}y^{6}\right)\left(\left(-x\right)y\right)^{3}}{\left(-x^{2}\right)^{3}y^{10}}$$

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

$$\frac{\left(-x^{2}y^{6}\right)\left(\left(-x\right)y\right)^{3}}{\left(-x^{2}\right)^{3}y^{10}}$$

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

$$\frac{\left(-x^{2}y^{6}\right)\left(-x\right)^{3}y^{3}}{\left(-x^{2}\right)^{3}y^{10}}$$

Cancel out y^{3} in both numerator and denominator.

$$\frac{\left(-x\right)^{3}\left(-x^{2}y^{6}\right)}{\left(-x^{2}\right)^{3}y^{7}}$$

Factor the expressions that are not already factored.

$$\frac{-x^{2}\left(-x\right)^{3}y^{6}}{\left(-x^{2}\right)^{3}y^{7}}$$

Cancel out y^{6} in both numerator and denominator.

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

Expand the expression.

$$\frac{x^{5}}{-yx^{6}}$$

Cancel out x^{5} in both numerator and denominator.

$$\frac{1}{-xy}$$