Solve 3*{left(left(2*3right)^-11/2^3right)}^-1*left(3*2^2right)^-2

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

Evaluate

$$1$$

Solution Steps

Multiply 2 and 3 to get 6.

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

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

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

Calculate 2 to the power of 3 and get 8.

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

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

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

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

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

Multiply 3 and 48 to get 144.

$$144\times \left(3\times 2^{2}\right)^{-2}$$

Calculate 2 to the power of 2 and get 4.

$$144\times \left(3\times 4\right)^{-2}$$

Multiply 3 and 4 to get 12.

$$144\times 12^{-2}$$

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

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

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

$$1$$

Factor

$$1$$