Solve 3^2left(2^-1right)^3{left(frac{1/3right)}^3{left(1/4right)}^-2}{6^-3}

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

Evaluate

$$144$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -1 and 3 to get -3.

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

Calculate 3 to the power of 2 and get 9.

$$\frac{9\times 2^{-3}\times \left(\frac{1}{3}\right)^{3}\times \left(\frac{1}{4}\right)^{-2}}{6^{-3}}$$

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$\frac{9\times \frac{1}{8}\times \left(\frac{1}{3}\right)^{3}\times \left(\frac{1}{4}\right)^{-2}}{6^{-3}}$$

Multiply 9 and \frac{1}{8} to get \frac{9}{8}.

$$\frac{\frac{9}{8}\times \left(\frac{1}{3}\right)^{3}\times \left(\frac{1}{4}\right)^{-2}}{6^{-3}}$$

Calculate \frac{1}{3} to the power of 3 and get \frac{1}{27}.

$$\frac{\frac{9}{8}\times \frac{1}{27}\times \left(\frac{1}{4}\right)^{-2}}{6^{-3}}$$

Multiply \frac{9}{8} and \frac{1}{27} to get \frac{1}{24}.

$$\frac{\frac{1}{24}\times \left(\frac{1}{4}\right)^{-2}}{6^{-3}}$$

Calculate \frac{1}{4} to the power of -2 and get 16.

$$\frac{\frac{1}{24}\times 16}{6^{-3}}$$

Multiply \frac{1}{24} and 16 to get \frac{2}{3}.

$$\frac{\frac{2}{3}}{6^{-3}}$$

Calculate 6 to the power of -3 and get \frac{1}{216}.

$$\frac{\frac{2}{3}}{\frac{1}{216}}$$

Divide \frac{2}{3} by \frac{1}{216} by multiplying \frac{2}{3} by the reciprocal of \frac{1}{216}.

$$\frac{2}{3}\times 216$$

Multiply \frac{2}{3} and 216 to get 144.

$$144$$

Factor

$$2^{4}\times 3^{2}$$