Solve ((2*3)^{-1}*1/2^3)^-1*(3*2^2)^-2=

$$( ( 2 \cdot 3 ) ^ { - 1 } \cdot \frac { 1 } { 2 ^ { 3 } } ) ^ { - 1 } \cdot ( 3 \cdot 2 ^ { 2 } ) ^ { - 2 } =$$

Evaluate

$$\frac{1}{3}\approx 0.333333333$$

Solution Steps

Multiply 2 and 3 to get 6.

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

Calculate 6 to the power of -1 and get \frac{1}{6}.

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

Calculate 2 to the power of 3 and get 8.

$$\left(\frac{1}{6}\times \frac{1}{8}\right)^{-1}\times \left(3\times 2^{2}\right)^{-2}$$

Multiply \frac{1}{6} and \frac{1}{8} to get \frac{1}{48}.

$$\left(\frac{1}{48}\right)^{-1}\times \left(3\times 2^{2}\right)^{-2}$$

Calculate \frac{1}{48} to the power of -1 and get 48.

$$48\times \left(3\times 2^{2}\right)^{-2}$$

Calculate 2 to the power of 2 and get 4.

$$48\times \left(3\times 4\right)^{-2}$$

Multiply 3 and 4 to get 12.

$$48\times 12^{-2}$$

Calculate 12 to the power of -2 and get \frac{1}{144}.

$$48\times \frac{1}{144}$$

Multiply 48 and \frac{1}{144} to get \frac{1}{3}.

$$\frac{1}{3}$$

Factor

$$\frac{1}{3} = 0.3333333333333333$$