Solve {left(9/4x^2right)}^2+{left(1/4x^2right)}^2

$${ \left( \frac{ 9 }{ 4 { x }^{ 2 } } \right) }^{ 2 } + { \left( \frac{ 1 }{ 4 { x }^{ 2 } } \right) }^{ 2 }$$

Evaluate

$$\frac{41}{8x^{4}}$$

Short Solution Steps

To raise \frac{9}{4x^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{9^{2}}{\left(4x^{2}\right)^{2}}+\left(\frac{1}{4x^{2}}\right)^{2}$$

To raise \frac{1}{4x^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{9^{2}}{\left(4x^{2}\right)^{2}}+\frac{1^{2}}{\left(4x^{2}\right)^{2}}$$

Since \frac{9^{2}}{\left(4x^{2}\right)^{2}} and \frac{1^{2}}{\left(4x^{2}\right)^{2}} have the same denominator, add them by adding their numerators.

$$\frac{9^{2}+1^{2}}{\left(4x^{2}\right)^{2}}$$

Do the calculations in 9^{2}+1^{2}.

$$\frac{82}{\left(4x^{2}\right)^{2}}$$

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

$$\frac{82}{16x^{4}}$$

Expand

$$\frac{41}{8x^{4}}$$

Short Solution Steps

To raise \frac{9}{4x^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{9^{2}}{\left(4x^{2}\right)^{2}}+\left(\frac{1}{4x^{2}}\right)^{2}$$

To raise \frac{1}{4x^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{9^{2}}{\left(4x^{2}\right)^{2}}+\frac{1^{2}}{\left(4x^{2}\right)^{2}}$$

Since \frac{9^{2}}{\left(4x^{2}\right)^{2}} and \frac{1^{2}}{\left(4x^{2}\right)^{2}} have the same denominator, add them by adding their numerators.

$$\frac{9^{2}+1^{2}}{\left(4x^{2}\right)^{2}}$$

Do the calculations in 9^{2}+1^{2}.

$$\frac{82}{\left(4x^{2}\right)^{2}}$$

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

$$\frac{82}{16x^{4}}$$