Solve 3xy/3xy(-2x)^3*(-1/4y^2)^2=

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

Evaluate

$$-\frac{x^{3}y^{4}}{2}$$

Solution Steps

Divide 3xy by 3xy to get 1.

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

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

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

Calculate -2 to the power of 3 and get -8.

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

Multiply 1 and -8 to get -8.

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

Expand \left(-\frac{1}{4}y^{2}\right)^{2}.

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

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

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

Calculate -\frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$-8x^{3}\times \frac{1}{16}y^{4}$$

Multiply -8 and \frac{1}{16} to get -\frac{1}{2}.

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

Expand

$$-\frac{x^{3}y^{4}}{2}$$

Solution Steps

Divide 3xy by 3xy to get 1.

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

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

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

Calculate -2 to the power of 3 and get -8.

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

Multiply 1 and -8 to get -8.

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

Expand \left(-\frac{1}{4}y^{2}\right)^{2}.

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

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

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

Calculate -\frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$-8x^{3}\times \frac{1}{16}y^{4}$$

Multiply -8 and \frac{1}{16} to get -\frac{1}{2}.

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