Solve (-4xy^3)*(-1/8xy)-(1/2xy^2)^2

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

Evaluate

$$\frac{x^{2}y^{4}}{4}$$

Solution Steps

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

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

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

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

Multiply -4 and -\frac{1}{8} to get \frac{1}{2}.

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

Expand \left(\frac{1}{2}xy^{2}\right)^{2}.

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

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

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

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{1}{2}x^{2}y^{4}-\frac{1}{4}x^{2}y^{4}$$

Combine \frac{1}{2}x^{2}y^{4} and -\frac{1}{4}x^{2}y^{4} to get \frac{1}{4}x^{2}y^{4}.

$$\frac{1}{4}x^{2}y^{4}$$

Expand

$$\frac{x^{2}y^{4}}{4}$$

Solution Steps

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

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

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

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

Multiply -4 and -\frac{1}{8} to get \frac{1}{2}.

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

Expand \left(\frac{1}{2}xy^{2}\right)^{2}.

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

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

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

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{1}{2}x^{2}y^{4}-\frac{1}{4}x^{2}y^{4}$$

Combine \frac{1}{2}x^{2}y^{4} and -\frac{1}{4}x^{2}y^{4} to get \frac{1}{4}x^{2}y^{4}.

$$\frac{1}{4}x^{2}y^{4}$$