Solve ((-2/3)^-2)^3*(1/3)^-4*3^-1*1/6

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

Evaluate

$$\frac{6561}{128}=51.2578125$$

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{729}{64}.

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

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

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

Multiply \frac{729}{64} and 81 to get \frac{59049}{64}.

$$\frac{59049}{64}\times 3^{-1}\times \frac{1}{6}$$

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

$$\frac{59049}{64}\times \frac{1}{3}\times \frac{1}{6}$$

Multiply \frac{59049}{64} and \frac{1}{3} to get \frac{19683}{64}.

$$\frac{19683}{64}\times \frac{1}{6}$$

Multiply \frac{19683}{64} and \frac{1}{6} to get \frac{6561}{128}.

$$\frac{6561}{128}$$

Factor

$$\frac{3 ^ {8}}{2 ^ {7}} = 51\frac{33}{128} = 51.2578125$$