Solve {left(sqrt{1/9+frac{6/18}}{{left(5-23/3right)}^2}right)}^3

$${ \left( \frac{ \sqrt{ \frac{ 1 }{ 9 } + \frac{ 6 }{ 18 } } }{ { \left(5- \frac{ 23 }{ 3 } \right) }^{ 2 } } \right) }^{ 3 }$$

Evaluate

$$\frac{27}{32768}=0.000823975$$

Solution Steps

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

$$\left(\frac{\sqrt{\frac{1}{9}+\frac{1}{3}}}{\left(5-\frac{23}{3}\right)^{2}}\right)^{3}$$

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

$$\left(\frac{\sqrt{\frac{4}{9}}}{\left(5-\frac{23}{3}\right)^{2}}\right)^{3}$$

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.

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

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

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

Calculate -\frac{8}{3} to the power of 2 and get \frac{64}{9}.

$$\left(\frac{\frac{2}{3}}{\frac{64}{9}}\right)^{3}$$

Divide \frac{2}{3} by \frac{64}{9} by multiplying \frac{2}{3} by the reciprocal of \frac{64}{9}.

$$\left(\frac{2}{3}\times \frac{9}{64}\right)^{3}$$

Multiply \frac{2}{3} and \frac{9}{64} to get \frac{3}{32}.

$$\left(\frac{3}{32}\right)^{3}$$

Calculate \frac{3}{32} to the power of 3 and get \frac{27}{32768}.

$$\frac{27}{32768}$$

Factor

$$\frac{3 ^ {3}}{2 ^ {15}} = 0.000823974609375$$