Solve (1/x^2)^2+(x^-2)^-2=

$$( \frac { 1 } { x ^ { 2 } } ) ^ { 2 } + ( x ^ { - 2 } ) ^ { - 2 } =$$

Evaluate

$$x^{4}+\frac{1}{x^{4}}$$

Short Solution Steps

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

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

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

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

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{4} times \frac{\left(x^{2}\right)^{2}}{\left(x^{2}\right)^{2}}.

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

Since \frac{1^{2}}{\left(x^{2}\right)^{2}} and \frac{x^{4}\left(x^{2}\right)^{2}}{\left(x^{2}\right)^{2}} have the same denominator, add them by adding their numerators.

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

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

$$\frac{1^{2}}{x^{4}}+x^{4}$$

Calculate 1 to the power of 2 and get 1.

$$\frac{1}{x^{4}}+x^{4}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{4} times \frac{x^{4}}{x^{4}}.

$$\frac{1}{x^{4}}+\frac{x^{4}x^{4}}{x^{4}}$$

Since \frac{1}{x^{4}} and \frac{x^{4}x^{4}}{x^{4}} have the same denominator, add them by adding their numerators.

$$\frac{1+x^{4}x^{4}}{x^{4}}$$

Do the multiplications in 1+x^{4}x^{4}.

$$\frac{1+x^{8}}{x^{4}}$$

Factor

$$\frac{x^{8}+1}{x^{4}}$$