Solve [(1+1/3)^3*(3+1/3)^-3]:(1-1/5)^2(1/5)^-1

$$[ ( 1 + \frac { 1 } { 3 } ) ^ { 3 } \cdot ( 3 + \frac { 1 } { 3 } ) ^ { - 3 } ] : ( 1 - \frac { 1 } { 5 } ) ^ { 2 } ( \frac { 1 } { 5 } ) ^ { - 1 }$$

Evaluate

$$\frac{1}{2}=0.5$$

Solution Steps

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

$$\frac{\left(\frac{4}{3}\right)^{3}\left(3+\frac{1}{3}\right)^{-3}}{\left(1-\frac{1}{5}\right)^{2}}\times \left(\frac{1}{5}\right)^{-1}$$

Calculate \frac{4}{3} to the power of 3 and get \frac{64}{27}.

$$\frac{\frac{64}{27}\left(3+\frac{1}{3}\right)^{-3}}{\left(1-\frac{1}{5}\right)^{2}}\times \left(\frac{1}{5}\right)^{-1}$$

Add 3 and \frac{1}{3} to get \frac{10}{3}.

$$\frac{\frac{64}{27}\times \left(\frac{10}{3}\right)^{-3}}{\left(1-\frac{1}{5}\right)^{2}}\times \left(\frac{1}{5}\right)^{-1}$$

Calculate \frac{10}{3} to the power of -3 and get \frac{27}{1000}.

$$\frac{\frac{64}{27}\times \frac{27}{1000}}{\left(1-\frac{1}{5}\right)^{2}}\times \left(\frac{1}{5}\right)^{-1}$$

Multiply \frac{64}{27} and \frac{27}{1000} to get \frac{8}{125}.

$$\frac{\frac{8}{125}}{\left(1-\frac{1}{5}\right)^{2}}\times \left(\frac{1}{5}\right)^{-1}$$

Subtract \frac{1}{5} from 1 to get \frac{4}{5}.

$$\frac{\frac{8}{125}}{\left(\frac{4}{5}\right)^{2}}\times \left(\frac{1}{5}\right)^{-1}$$

Calculate \frac{4}{5} to the power of 2 and get \frac{16}{25}.

$$\frac{\frac{8}{125}}{\frac{16}{25}}\times \left(\frac{1}{5}\right)^{-1}$$

Divide \frac{8}{125} by \frac{16}{25} by multiplying \frac{8}{125} by the reciprocal of \frac{16}{25}.

$$\frac{8}{125}\times \frac{25}{16}\times \left(\frac{1}{5}\right)^{-1}$$

Multiply \frac{8}{125} and \frac{25}{16} to get \frac{1}{10}.

$$\frac{1}{10}\times \left(\frac{1}{5}\right)^{-1}$$

Calculate \frac{1}{5} to the power of -1 and get 5.

$$\frac{1}{10}\times 5$$

Multiply \frac{1}{10} and 5 to get \frac{1}{2}.

$$\frac{1}{2}$$

Factor

$$\frac{1}{2} = 0.5$$