Solve (frac{3sqrt{10}}{10})^2

$$( \frac { 3 \sqrt { 10 } } { 10 } ) ^ { 2 }$$

Evaluate

$$\frac{9}{10}=0.9$$

Solution Steps

To raise \frac{3\sqrt{10}}{10} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(3\sqrt{10}\right)^{2}}{10^{2}}$$

Expand \left(3\sqrt{10}\right)^{2}.

$$\frac{3^{2}\left(\sqrt{10}\right)^{2}}{10^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9\left(\sqrt{10}\right)^{2}}{10^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{9\times 10}{10^{2}}$$

Multiply 9 and 10 to get 90.

$$\frac{90}{10^{2}}$$

Calculate 10 to the power of 2 and get 100.

$$\frac{90}{100}$$

Reduce the fraction \frac{90}{100} to lowest terms by extracting and canceling out 10.

$$\frac{9}{10}$$

Factor

$$\frac{3 ^ {2}}{2 \cdot 5} = 0.9$$