Solve {left({left(2/3right)}^2right)}^3{left(1/3right)}^-43^-1*1/6

$${ \left( { \left( \frac{ 2 }{ 3 } \right) }^{ 2 } \right) }^{ 3 } { \left( \frac{ 1 }{ 3 } \right) }^{ -4 } { 3 }^{ -1 } \times \frac{ 1 }{ 6 }$$

Evaluate

$$\frac{32}{81}\approx 0.395061728$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\left(\frac{2}{3}\right)^{6}\times \left(\frac{1}{3}\right)^{-4}\times 3^{-1}\times \frac{1}{6}$$

Calculate \frac{2}{3} to the power of 6 and get \frac{64}{729}.

$$\frac{64}{729}\times \left(\frac{1}{3}\right)^{-4}\times 3^{-1}\times \frac{1}{6}$$

Calculate \frac{1}{3} to the power of -4 and get 81.

$$\frac{64}{729}\times 81\times 3^{-1}\times \frac{1}{6}$$

Multiply \frac{64}{729} and 81 to get \frac{64}{9}.

$$\frac{64}{9}\times 3^{-1}\times \frac{1}{6}$$

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

$$\frac{64}{9}\times \frac{1}{3}\times \frac{1}{6}$$

Multiply \frac{64}{9} and \frac{1}{3} to get \frac{64}{27}.

$$\frac{64}{27}\times \frac{1}{6}$$

Multiply \frac{64}{27} and \frac{1}{6} to get \frac{32}{81}.

$$\frac{32}{81}$$

Factor

$$\frac{2 ^ {5}}{3 ^ {4}} = 0.3950617283950617$$