Solve 16^{-frac{2/2}27^{-1}81^frac{1{4}}}{16^-227^-frac{4{2}}81^frac{2{4}}}

$$\frac { 16 ^ { - \frac { 2 } { 2 } } 27 ^ { - 1 } 81 ^ { \frac { 1 } { 4 } } } { 16 ^ { - 2 } 27 ^ { - \frac { 4 } { 2 } } 81 ^ { \frac { 2 } { 4 } } }$$

Evaluate

$$144$$

Solution Steps

Divide 2 by 2 to get 1.

$$\frac{16^{-1}\times 27^{-1}\times 81^{\frac{1}{4}}}{16^{-2}\times 27^{-\frac{4}{2}}\times 81^{\frac{2}{4}}}$$

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

$$\frac{\frac{1}{16}\times 27^{-1}\times 81^{\frac{1}{4}}}{16^{-2}\times 27^{-\frac{4}{2}}\times 81^{\frac{2}{4}}}$$

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

$$\frac{\frac{1}{16}\times \frac{1}{27}\times 81^{\frac{1}{4}}}{16^{-2}\times 27^{-\frac{4}{2}}\times 81^{\frac{2}{4}}}$$

Multiply \frac{1}{16} and \frac{1}{27} to get \frac{1}{432}.

$$\frac{\frac{1}{432}\times 81^{\frac{1}{4}}}{16^{-2}\times 27^{-\frac{4}{2}}\times 81^{\frac{2}{4}}}$$

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

$$\frac{\frac{1}{432}\times 3}{16^{-2}\times 27^{-\frac{4}{2}}\times 81^{\frac{2}{4}}}$$

Multiply \frac{1}{432} and 3 to get \frac{1}{144}.

$$\frac{\frac{1}{144}}{16^{-2}\times 27^{-\frac{4}{2}}\times 81^{\frac{2}{4}}}$$

Calculate 16 to the power of -2 and get \frac{1}{256}.

$$\frac{\frac{1}{144}}{\frac{1}{256}\times 27^{-\frac{4}{2}}\times 81^{\frac{2}{4}}}$$

Divide 4 by 2 to get 2.

$$\frac{\frac{1}{144}}{\frac{1}{256}\times 27^{-2}\times 81^{\frac{2}{4}}}$$

Calculate 27 to the power of -2 and get \frac{1}{729}.

$$\frac{\frac{1}{144}}{\frac{1}{256}\times \frac{1}{729}\times 81^{\frac{2}{4}}}$$

Multiply \frac{1}{256} and \frac{1}{729} to get \frac{1}{186624}.

$$\frac{\frac{1}{144}}{\frac{1}{186624}\times 81^{\frac{2}{4}}}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{1}{144}}{\frac{1}{186624}\times 81^{\frac{1}{2}}}$$

Calculate 81 to the power of \frac{1}{2} and get 9.

$$\frac{\frac{1}{144}}{\frac{1}{186624}\times 9}$$

Multiply \frac{1}{186624} and 9 to get \frac{1}{20736}.

$$\frac{\frac{1}{144}}{\frac{1}{20736}}$$

Divide \frac{1}{144} by \frac{1}{20736} by multiplying \frac{1}{144} by the reciprocal of \frac{1}{20736}.

$$\frac{1}{144}\times 20736$$

Multiply \frac{1}{144} and 20736 to get 144.

$$144$$

Factor

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