Solve (frac{9sqrt{13}}{13})^2

$$( \frac { 9 \sqrt { 13 } } { 13 } ) ^ { 2 }$$

Evaluate

$$\frac{81}{13}\approx 6.230769231$$

Solution Steps

To raise \frac{9\sqrt{13}}{13} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(9\sqrt{13}\right)^{2}}{13^{2}}$$

Expand \left(9\sqrt{13}\right)^{2}.

$$\frac{9^{2}\left(\sqrt{13}\right)^{2}}{13^{2}}$$

Calculate 9 to the power of 2 and get 81.

$$\frac{81\left(\sqrt{13}\right)^{2}}{13^{2}}$$

The square of \sqrt{13} is 13.

$$\frac{81\times 13}{13^{2}}$$

Multiply 81 and 13 to get 1053.

$$\frac{1053}{13^{2}}$$

Calculate 13 to the power of 2 and get 169.

$$\frac{1053}{169}$$

Reduce the fraction \frac{1053}{169} to lowest terms by extracting and canceling out 13.

$$\frac{81}{13}$$

Factor

$$\frac{3 ^ {4}}{13} = 6\frac{3}{13} = 6.230769230769231$$