Solve /3xyleft(-2xright)^3{left(-1/4y^2right)}^2

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

Evaluate

$$-\frac{x^{2}y^{3}}{6}$$

Solution Steps

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

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

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

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

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

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

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

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

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

$$\frac{1}{3xy}\left(-8\right)x^{3}\times \frac{1}{16}y^{4}$$

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

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

Multiply \frac{1}{3xy} times -\frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

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

Express \frac{-1}{3xy\times 2}x^{3} as a single fraction.

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

Cancel out x in both numerator and denominator.

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

Express \frac{-x^{2}}{2\times 3y}y^{4} as a single fraction.

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

Cancel out y in both numerator and denominator.

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

Multiply 2 and 3 to get 6.

$$\frac{-x^{2}y^{3}}{6}$$

Expand

$$-\frac{x^{2}y^{3}}{6}$$

Solution Steps

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

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

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

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

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

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

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

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

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

$$\frac{1}{3xy}\left(-8\right)x^{3}\times \frac{1}{16}y^{4}$$

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

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

Multiply \frac{1}{3xy} times -\frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

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

Express \frac{-1}{3xy\times 2}x^{3} as a single fraction.

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

Cancel out x in both numerator and denominator.

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

Express \frac{-x^{2}}{2\times 3y}y^{4} as a single fraction.

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

Cancel out y in both numerator and denominator.

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

Multiply 2 and 3 to get 6.

$$\frac{-x^{2}y^{3}}{6}$$