Solve {(81)^{-3/4}*frac{(16)^frac{1{4}}}{(6)^-2}*(1/27)^-frac{4{3}}}^frac{1{3}}

$$\{ ( 81 ) ^ { - \frac { 3 } { 4 } } \times \frac { ( 16 ) ^ { \frac { 1 } { 4 } } } { ( 6 ) ^ { - 2 } } \times ( \frac { 1 } { 27 } ) ^ { - \frac { 4 } { 3 } } \} ^ { \frac { 1 } { 3 } }$$

Evaluate

$$6$$

Solution Steps

Calculate 81 to the power of -\frac{3}{4} and get \frac{1}{27}.

$$\left(\frac{1}{27}\times \frac{16^{\frac{1}{4}}}{6^{-2}}\times \left(\frac{1}{27}\right)^{-\frac{4}{3}}\right)^{\frac{1}{3}}$$

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

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

Calculate 6 to the power of -2 and get \frac{1}{36}.

$$\left(\frac{1}{27}\times \frac{2}{\frac{1}{36}}\times \left(\frac{1}{27}\right)^{-\frac{4}{3}}\right)^{\frac{1}{3}}$$

Divide 2 by \frac{1}{36} by multiplying 2 by the reciprocal of \frac{1}{36}.

$$\left(\frac{1}{27}\times 2\times 36\times \left(\frac{1}{27}\right)^{-\frac{4}{3}}\right)^{\frac{1}{3}}$$

Multiply 2 and 36 to get 72.

$$\left(\frac{1}{27}\times 72\times \left(\frac{1}{27}\right)^{-\frac{4}{3}}\right)^{\frac{1}{3}}$$

Multiply \frac{1}{27} and 72 to get \frac{8}{3}.

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

Calculate \frac{1}{27} to the power of -\frac{4}{3} and get 81.

$$\left(\frac{8}{3}\times 81\right)^{\frac{1}{3}}$$

Multiply \frac{8}{3} and 81 to get 216.

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

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

$$6$$

Factor

$$2\times 3$$