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

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

Evaluate

$$-\frac{3x^{4}y^{5}}{2}$$

Solution Steps

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

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

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

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

Multiply 3 and -8 to get -24.

$$-24xyx^{3}\left(-\frac{1}{4}y^{2}\right)^{2}$$

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

$$-24x^{4}y\left(-\frac{1}{4}y^{2}\right)^{2}$$

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

$$-24x^{4}y\left(-\frac{1}{4}\right)^{2}\left(y^{2}\right)^{2}$$

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

$$-24x^{4}y\left(-\frac{1}{4}\right)^{2}y^{4}$$

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

$$-24x^{4}y\times \frac{1}{16}y^{4}$$

Multiply -24 and \frac{1}{16} to get -\frac{3}{2}.

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

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$-\frac{3}{2}x^{4}y^{5}$$

Expand

$$-\frac{3x^{4}y^{5}}{2}$$

Solution Steps

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

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

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

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

Multiply 3 and -8 to get -24.

$$-24xyx^{3}\left(-\frac{1}{4}y^{2}\right)^{2}$$

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

$$-24x^{4}y\left(-\frac{1}{4}y^{2}\right)^{2}$$

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

$$-24x^{4}y\left(-\frac{1}{4}\right)^{2}\left(y^{2}\right)^{2}$$

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

$$-24x^{4}y\left(-\frac{1}{4}\right)^{2}y^{4}$$

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

$$-24x^{4}y\times \frac{1}{16}y^{4}$$

Multiply -24 and \frac{1}{16} to get -\frac{3}{2}.

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

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$-\frac{3}{2}x^{4}y^{5}$$