Solve [(-1/2x^2y)^2]^2=

$$[ ( - \frac { 1 } { 2 } x ^ { 2 } y ) ^ { 2 } ] ^ { 2 } =$$

Evaluate

$$\frac{y^{4}x^{8}}{16}$$

Solution Steps

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

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

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

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

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

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

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

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

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

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

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

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

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

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

Expand

$$\frac{y^{4}x^{8}}{16}$$

Solution Steps

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

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

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

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

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

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

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

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

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

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

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

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

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

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