Solve (-xy/2xy^4)^2

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

Evaluate

$$\frac{1}{4y^{6}}$$

Solution Steps

Cancel out xy in both numerator and denominator.

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

Calculate -\frac{1}{2y^{3}} to the power of 2 and get \left(\frac{1}{2y^{3}}\right)^{2}.

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

To raise \frac{1}{2y^{3}} to a power, raise both numerator and denominator to the power and then divide.

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

Calculate 1 to the power of 2 and get 1.

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

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{1}{2^{2}y^{6}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{1}{4y^{6}}$$

Expand

$$\frac{1}{4y^{6}}$$

Solution Steps

Cancel out xy in both numerator and denominator.

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

Calculate -\frac{1}{2y^{3}} to the power of 2 and get \left(\frac{1}{2y^{3}}\right)^{2}.

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

To raise \frac{1}{2y^{3}} to a power, raise both numerator and denominator to the power and then divide.

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

Calculate 1 to the power of 2 and get 1.

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

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{1}{2^{2}y^{6}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{1}{4y^{6}}$$