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

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

Evaluate

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

Short Solution Steps

Divide n by \frac{\left(\left(-x^{2}\right)y^{0}\right)^{-3}}{-2x\left(\left(-x\right)y\right)^{-1}} by multiplying n by the reciprocal of \frac{\left(\left(-x^{2}\right)y^{0}\right)^{-3}}{-2x\left(\left(-x\right)y\right)^{-1}}.

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

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

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

Calculate y to the power of 0 and get 1.

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

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

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

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

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

Cancel out 1 in both numerator and denominator.

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

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

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

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

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

Multiply -2 and -1 to get 2.

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

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

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

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

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

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

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

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

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

Cancel out -1 in both numerator and denominator.

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

Expand

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

Short Solution Steps

Divide n by \frac{\left(\left(-x^{2}\right)y^{0}\right)^{-3}}{-2x\left(\left(-x\right)y\right)^{-1}} by multiplying n by the reciprocal of \frac{\left(\left(-x^{2}\right)y^{0}\right)^{-3}}{-2x\left(\left(-x\right)y\right)^{-1}}.

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

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

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

Calculate y to the power of 0 and get 1.

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

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

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

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

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

Cancel out 1 in both numerator and denominator.

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

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

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

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

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

Multiply -2 and -1 to get 2.

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

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

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

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

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

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

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

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

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

Cancel out -1 in both numerator and denominator.

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