Solve {left(sqrt{1/9+frac{6/18}}{5-23/3}right)}^3

$${ \left( \frac{ \sqrt{ \frac{ 1 }{ 9 } + \frac{ 6 }{ 18 } } }{ 5- \frac{ 23 }{ 3 } } \right) }^{ 3 }$$

Evaluate

$$-\frac{1}{64}=-0.015625$$

Solution Steps

Reduce the fraction \frac{6}{18} to lowest terms by extracting and canceling out 6.

$$\left(\frac{\sqrt{\frac{1}{9}+\frac{1}{3}}}{5-\frac{23}{3}}\right)^{3}$$

Add \frac{1}{9} and \frac{1}{3} to get \frac{4}{9}.

$$\left(\frac{\sqrt{\frac{4}{9}}}{5-\frac{23}{3}}\right)^{3}$$

Rewrite the square root of the division \frac{4}{9} as the division of square roots \frac{\sqrt{4}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$\left(\frac{\frac{2}{3}}{5-\frac{23}{3}}\right)^{3}$$

Subtract \frac{23}{3} from 5 to get -\frac{8}{3}.

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

Divide \frac{2}{3} by -\frac{8}{3} by multiplying \frac{2}{3} by the reciprocal of -\frac{8}{3}.

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

Multiply \frac{2}{3} and -\frac{3}{8} to get -\frac{1}{4}.

$$\left(-\frac{1}{4}\right)^{3}$$

Calculate -\frac{1}{4} to the power of 3 and get -\frac{1}{64}.

$$-\frac{1}{64}$$

Factor

$$-\frac{1}{64} = -0.015625$$