Solve (frac{8sqrt{3}}{3})^2-16

$$( \frac { 8 \sqrt { 3 } } { 3 } ) ^ { 2 } - 16$$

Evaluate

$$\frac{16}{3}\approx 5.333333333$$

Solution Steps

To raise \frac{8\sqrt{3}}{3} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(8\sqrt{3}\right)^{2}}{3^{2}}-16$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 16 times \frac{3^{2}}{3^{2}}.

$$\frac{\left(8\sqrt{3}\right)^{2}}{3^{2}}-\frac{16\times 3^{2}}{3^{2}}$$

Since \frac{\left(8\sqrt{3}\right)^{2}}{3^{2}} and \frac{16\times 3^{2}}{3^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(8\sqrt{3}\right)^{2}-16\times 3^{2}}{3^{2}}$$

Expand \left(8\sqrt{3}\right)^{2}.

$$\frac{8^{2}\left(\sqrt{3}\right)^{2}}{3^{2}}-16$$

Calculate 8 to the power of 2 and get 64.

$$\frac{64\left(\sqrt{3}\right)^{2}}{3^{2}}-16$$

The square of \sqrt{3} is 3.

$$\frac{64\times 3}{3^{2}}-16$$

Multiply 64 and 3 to get 192.

$$\frac{192}{3^{2}}-16$$

Calculate 3 to the power of 2 and get 9.

$$\frac{192}{9}-16$$

Reduce the fraction \frac{192}{9} to lowest terms by extracting and canceling out 3.

$$\frac{64}{3}-16$$

Subtract 16 from \frac{64}{3} to get \frac{16}{3}.

$$\frac{16}{3}$$

Factor

$$\frac{2 ^ {4}}{3} = 5\frac{1}{3} = 5.333333333333333$$