Solve left(-x^2yright)^2div1/2xy^2*-2xy

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

Evaluate

$$-4y^{5}x^{6}$$

Solution Steps

Multiply x and x to get x^{2}.

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

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

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

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

Calculate -x^{2} to the power of 2 and get \left(x^{2}\right)^{2}.

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

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

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

Divide x^{4}y^{2} by \frac{1}{2} by multiplying x^{4}y^{2} by the reciprocal of \frac{1}{2}.

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

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

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

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$x^{6}y^{5}\times 2\left(-2\right)$$

Multiply 2 and -2 to get -4.

$$x^{6}y^{5}\left(-4\right)$$

Expand

$$-4y^{5}x^{6}$$

Solution Steps

Multiply x and x to get x^{2}.

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

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

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

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

Calculate -x^{2} to the power of 2 and get \left(x^{2}\right)^{2}.

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

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

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

Divide x^{4}y^{2} by \frac{1}{2} by multiplying x^{4}y^{2} by the reciprocal of \frac{1}{2}.

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

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

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

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$x^{6}y^{5}\times 2\left(-2\right)$$

Multiply 2 and -2 to get -4.

$$x^{6}y^{5}\left(-4\right)$$