Solve (-x^{2}y)^4div(x^2y)-(-x^2y)^3

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

Evaluate

$$2y^{3}x^{6}$$

Short Solution Steps

Expand \left(\left(-x^{2}\right)y\right)^{4}.

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

Cancel out y in both numerator and denominator.

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

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

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

To add or subtract expressions, expand them to make their denominators the same. Multiply \left(-x^{2}\right)^{3}y^{3} times \frac{x^{2}}{x^{2}}.

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

Since \frac{y^{3}\left(-x^{2}\right)^{4}}{x^{2}} and \frac{\left(-x^{2}\right)^{3}y^{3}x^{2}}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

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

Expand \left(-x^{2}\right)^{4}.

$$\frac{y^{3}\left(-1\right)^{4}\left(x^{2}\right)^{4}}{x^{2}}-\left(-x^{2}\right)^{3}y^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$\frac{y^{3}\left(-1\right)^{4}x^{8}}{x^{2}}-\left(-x^{2}\right)^{3}y^{3}$$

Calculate -1 to the power of 4 and get 1.

$$\frac{y^{3}\times 1x^{8}}{x^{2}}-\left(-x^{2}\right)^{3}y^{3}$$

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

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

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

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

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

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

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

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

Multiply -1 and -1 to get 1.

$$y^{3}x^{6}+x^{6}y^{3}$$

Combine y^{3}x^{6} and x^{6}y^{3} to get 2y^{3}x^{6}.

$$2y^{3}x^{6}$$

Expand

$$2y^{3}x^{6}$$

Short Solution Steps

Expand \left(\left(-x^{2}\right)y\right)^{4}.

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

Cancel out y in both numerator and denominator.

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

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

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

To add or subtract expressions, expand them to make their denominators the same. Multiply \left(-x^{2}\right)^{3}y^{3} times \frac{x^{2}}{x^{2}}.

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

Since \frac{y^{3}\left(-x^{2}\right)^{4}}{x^{2}} and \frac{\left(-x^{2}\right)^{3}y^{3}x^{2}}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

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

Expand \left(-x^{2}\right)^{4}.

$$\frac{y^{3}\left(-1\right)^{4}\left(x^{2}\right)^{4}}{x^{2}}-\left(-x^{2}\right)^{3}y^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$\frac{y^{3}\left(-1\right)^{4}x^{8}}{x^{2}}-\left(-x^{2}\right)^{3}y^{3}$$

Calculate -1 to the power of 4 and get 1.

$$\frac{y^{3}\times 1x^{8}}{x^{2}}-\left(-x^{2}\right)^{3}y^{3}$$

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

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

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

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

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

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

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

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

Multiply -1 and -1 to get 1.

$$y^{3}x^{6}+x^{6}y^{3}$$

Combine y^{3}x^{6} and x^{6}y^{3} to get 2y^{3}x^{6}.

$$2y^{3}x^{6}$$