Solve (frac{10*sqrt{3}}{3})^2)^-1=

$$( \frac { 10 \cdot \sqrt { 3 } } { 3 } ) ^ { 2 } ) ^ { - 1 } =$$

Evaluate

$$\frac{100}{3}\approx 33.333333333$$

Solution Steps

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

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

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

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

Calculate 10 to the power of 2 and get 100.

$$\frac{100\left(\sqrt{3}\right)^{2}}{3^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{100\times 3}{3^{2}}$$

Multiply 100 and 3 to get 300.

$$\frac{300}{3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{300}{9}$$

Reduce the fraction \frac{300}{9} to lowest terms by extracting and canceling out 3.

$$\frac{100}{3}$$

Factor

$$\frac{2 ^ {2} \cdot 5 ^ {2}}{3} = 33\frac{1}{3} = 33.333333333333336$$