Solve (-x^2/2x^2)^2

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

Evaluate

$$\frac{1}{4}=0.25$$

Solution Steps

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

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

Calculate -x^{2} to the power of 2 and get \left(x^{2}\right)^{2}.

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

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

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

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

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

Calculate 2 to the power of 2 and get 4.

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

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

$$\frac{x^{4}}{4x^{4}}$$

Cancel out x^{4} in both numerator and denominator.

$$\frac{1}{4}$$

Factor

$$\frac{1}{2 ^ {2}} = 0.25$$