Solve (4)(-2x^2y^3)^2div(-xy)^3

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

Evaluate

$$-16xy^{3}$$

Solution Steps

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

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

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

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

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

$$\frac{4\left(-2\right)^{2}x^{4}y^{6}}{\left(\left(-x\right)y\right)^{3}}$$

Calculate -2 to the power of 2 and get 4.

$$\frac{4\times 4x^{4}y^{6}}{\left(\left(-x\right)y\right)^{3}}$$

Multiply 4 and 4 to get 16.

$$\frac{16x^{4}y^{6}}{\left(\left(-x\right)y\right)^{3}}$$

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

$$\frac{16x^{4}y^{6}}{\left(-x\right)^{3}y^{3}}$$

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

$$\frac{16y^{3}x^{4}}{\left(-x\right)^{3}}$$

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

$$\frac{16y^{3}x^{4}}{\left(-1\right)^{3}x^{3}}$$

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

$$\frac{16y^{3}x^{4}}{-x^{3}}$$

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

$$\frac{16xy^{3}}{-1}$$

Anything divided by -1 gives its opposite.

$$-16xy^{3}$$

Expand

$$-16xy^{3}$$

Solution Steps

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

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

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

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

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

$$\frac{4\left(-2\right)^{2}x^{4}y^{6}}{\left(\left(-x\right)y\right)^{3}}$$

Calculate -2 to the power of 2 and get 4.

$$\frac{4\times 4x^{4}y^{6}}{\left(\left(-x\right)y\right)^{3}}$$

Multiply 4 and 4 to get 16.

$$\frac{16x^{4}y^{6}}{\left(\left(-x\right)y\right)^{3}}$$

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

$$\frac{16x^{4}y^{6}}{\left(-x\right)^{3}y^{3}}$$

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

$$\frac{16y^{3}x^{4}}{\left(-x\right)^{3}}$$

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

$$\frac{16y^{3}x^{4}}{\left(-1\right)^{3}x^{3}}$$

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

$$\frac{16y^{3}x^{4}}{-x^{3}}$$

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

$$\frac{16xy^{3}}{-1}$$

Anything divided by -1 gives its opposite.

$$-16xy^{3}$$