Solve 2x^3*(-2xy)*(-1/2xy)^3

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

Evaluate

$$\frac{y^{4}x^{7}}{2}$$

Solution Steps

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

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

Multiply 2 and -2 to get -4.

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

Expand \left(-\frac{1}{2}xy\right)^{3}.

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

Calculate -\frac{1}{2} to the power of 3 and get -\frac{1}{8}.

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

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

$$\frac{1}{2}x^{4}yx^{3}y^{3}$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$\frac{1}{2}x^{7}yy^{3}$$

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

$$\frac{1}{2}x^{7}y^{4}$$

Expand

$$\frac{y^{4}x^{7}}{2}$$

Solution Steps

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

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

Multiply 2 and -2 to get -4.

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

Expand \left(-\frac{1}{2}xy\right)^{3}.

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

Calculate -\frac{1}{2} to the power of 3 and get -\frac{1}{8}.

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

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

$$\frac{1}{2}x^{4}yx^{3}y^{3}$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$\frac{1}{2}x^{7}yy^{3}$$

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

$$\frac{1}{2}x^{7}y^{4}$$