Solve (-x^2y^0)^-3/(-2x)(-xy)^-1

$$\frac { ( - x ^ { 2 } y ^ { 0 } ) ^ { - 3 } } { ( - 2 x ) ( - x y ) ^ { - 1 } }$$

Evaluate

$$-\frac{y}{2x^{6}}$$

Short Solution Steps

Calculate y to the power of 0 and get 1.

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

Expand \left(\left(-x^{2}\right)\times 1\right)^{-3}.

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

Calculate 1 to the power of -3 and get 1.

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

Expand \left(\left(-x\right)y\right)^{-1}.

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

Cancel out 1 in both numerator and denominator.

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

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

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

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

$$\frac{\left(-1\right)^{-3}x^{-6}}{-2x\left(-x\right)^{-1}y^{-1}}$$

Calculate -1 to the power of -3 and get -1.

$$\frac{-x^{-6}}{-2x\left(-x\right)^{-1}y^{-1}}$$

Expand \left(-x\right)^{-1}.

$$\frac{-x^{-6}}{-2x\left(-1\right)^{-1}x^{-1}y^{-1}}$$

Calculate -1 to the power of -1 and get -1.

$$\frac{-x^{-6}}{-2x\left(-1\right)x^{-1}y^{-1}}$$

Multiply -2 and -1 to get 2.

$$\frac{-x^{-6}}{2xx^{-1}y^{-1}}$$

Multiply x and x^{-1} to get 1.

$$\frac{-x^{-6}}{2y^{-1}}$$

Cancel out -1 in both numerator and denominator.

$$\frac{x^{-6}}{-2y^{-1}}$$

Expand

$$-\frac{y}{2x^{6}}$$

Short Solution Steps

Calculate y to the power of 0 and get 1.

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

Expand \left(\left(-x^{2}\right)\times 1\right)^{-3}.

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

Calculate 1 to the power of -3 and get 1.

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

Expand \left(\left(-x\right)y\right)^{-1}.

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

Cancel out 1 in both numerator and denominator.

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

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

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

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

$$\frac{\left(-1\right)^{-3}x^{-6}}{-2x\left(-x\right)^{-1}y^{-1}}$$

Calculate -1 to the power of -3 and get -1.

$$\frac{-x^{-6}}{-2x\left(-x\right)^{-1}y^{-1}}$$

Expand \left(-x\right)^{-1}.

$$\frac{-x^{-6}}{-2x\left(-1\right)^{-1}x^{-1}y^{-1}}$$

Calculate -1 to the power of -1 and get -1.

$$\frac{-x^{-6}}{-2x\left(-1\right)x^{-1}y^{-1}}$$

Multiply -2 and -1 to get 2.

$$\frac{-x^{-6}}{2xx^{-1}y^{-1}}$$

Multiply x and x^{-1} to get 1.

$$\frac{-x^{-6}}{2y^{-1}}$$

Cancel out -1 in both numerator and denominator.

$$\frac{x^{-6}}{-2y^{-1}}$$