Solve {left(frac{2sqrt{2}}{3}right)}^2

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

Evaluate

$$\frac{8}{9}\approx 0.888888889$$

Solution Steps

To raise \frac{2\sqrt{2}}{3} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

Calculate 2 to the power of 2 and get 4.

$$\frac{4\left(\sqrt{2}\right)^{2}}{3^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{4\times 2}{3^{2}}$$

Multiply 4 and 2 to get 8.

$$\frac{8}{3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{8}{9}$$

Factor

$$\frac{2 ^ {3}}{3 ^ {2}} = 0.8888888888888888$$