Solve frac{(4^-2*3^-6)*sqrt[4]{16}}{(64*729*8)^-frac{1{3}}}

$$\frac { ( 4 ^ { - 2 } \times 3 ^ { - 6 } ) \times \sqrt[ 4 ] { 16 } } { ( 64 \times 729 \times 8 ) ^ { - \frac { 1 } { 3 } } }$$

Evaluate

$$\frac{1}{81}\approx 0.012345679$$

Solution Steps

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

$$\frac{\frac{1}{16}\times 3^{-6}\sqrt[4]{16}}{\left(64\times 729\times 8\right)^{-\frac{1}{3}}}$$

Calculate 3 to the power of -6 and get \frac{1}{729}.

$$\frac{\frac{1}{16}\times \frac{1}{729}\sqrt[4]{16}}{\left(64\times 729\times 8\right)^{-\frac{1}{3}}}$$

Multiply \frac{1}{16} and \frac{1}{729} to get \frac{1}{11664}.

$$\frac{\frac{1}{11664}\sqrt[4]{16}}{\left(64\times 729\times 8\right)^{-\frac{1}{3}}}$$

Calculate \sqrt[4]{16} and get 2.

$$\frac{\frac{1}{11664}\times 2}{\left(64\times 729\times 8\right)^{-\frac{1}{3}}}$$

Multiply \frac{1}{11664} and 2 to get \frac{1}{5832}.

$$\frac{\frac{1}{5832}}{\left(64\times 729\times 8\right)^{-\frac{1}{3}}}$$

Multiply 64 and 729 to get 46656.

$$\frac{\frac{1}{5832}}{\left(46656\times 8\right)^{-\frac{1}{3}}}$$

Multiply 46656 and 8 to get 373248.

$$\frac{\frac{1}{5832}}{373248^{-\frac{1}{3}}}$$

Calculate 373248 to the power of -\frac{1}{3} and get \frac{1}{72}.

$$\frac{\frac{1}{5832}}{\frac{1}{72}}$$

Divide \frac{1}{5832} by \frac{1}{72} by multiplying \frac{1}{5832} by the reciprocal of \frac{1}{72}.

$$\frac{1}{5832}\times 72$$

Multiply \frac{1}{5832} and 72 to get \frac{1}{81}.

$$\frac{1}{81}$$

Factor

$$\frac{1}{3 ^ {4}} = 0.012345679012345678$$