Solve (64)^{frac{-1/6}*(216)^{-1/3}*(81)^frac{1{4}}}{(512)^frac{-1{3}}*(16)^frac{1{4}}*(9)^frac{-1{2}}}

$$\frac { ( 64 ) ^ { \frac { - 1 } { 6 } } \times ( 216 ) ^ { \frac { - 1 } { 3 } } \times ( 81 ) ^ { \frac { 1 } { 4 } } } { ( 512 ) ^ { \frac { - 1 } { 3 } } \times ( 16 ) ^ { \frac { 1 } { 4 } } \times ( 9 ) ^ { \frac { - 1 } { 2 } } }$$

Evaluate

$$3$$

Solution Steps

Fraction \frac{-1}{6} can be rewritten as -\frac{1}{6} by extracting the negative sign.

$$\frac{64^{-\frac{1}{6}}\times 216^{\frac{-1}{3}}\times 81^{\frac{1}{4}}}{512^{\frac{-1}{3}}\times 16^{\frac{1}{4}}\times 9^{\frac{-1}{2}}}$$

Calculate 64 to the power of -\frac{1}{6} and get \frac{1}{2}.

$$\frac{\frac{1}{2}\times 216^{\frac{-1}{3}}\times 81^{\frac{1}{4}}}{512^{\frac{-1}{3}}\times 16^{\frac{1}{4}}\times 9^{\frac{-1}{2}}}$$

Fraction \frac{-1}{3} can be rewritten as -\frac{1}{3} by extracting the negative sign.

$$\frac{\frac{1}{2}\times 216^{-\frac{1}{3}}\times 81^{\frac{1}{4}}}{512^{\frac{-1}{3}}\times 16^{\frac{1}{4}}\times 9^{\frac{-1}{2}}}$$

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

$$\frac{\frac{1}{2}\times \frac{1}{6}\times 81^{\frac{1}{4}}}{512^{\frac{-1}{3}}\times 16^{\frac{1}{4}}\times 9^{\frac{-1}{2}}}$$

Multiply \frac{1}{2} and \frac{1}{6} to get \frac{1}{12}.

$$\frac{\frac{1}{12}\times 81^{\frac{1}{4}}}{512^{\frac{-1}{3}}\times 16^{\frac{1}{4}}\times 9^{\frac{-1}{2}}}$$

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

$$\frac{\frac{1}{12}\times 3}{512^{\frac{-1}{3}}\times 16^{\frac{1}{4}}\times 9^{\frac{-1}{2}}}$$

Multiply \frac{1}{12} and 3 to get \frac{1}{4}.

$$\frac{\frac{1}{4}}{512^{\frac{-1}{3}}\times 16^{\frac{1}{4}}\times 9^{\frac{-1}{2}}}$$

Fraction \frac{-1}{3} can be rewritten as -\frac{1}{3} by extracting the negative sign.

$$\frac{\frac{1}{4}}{512^{-\frac{1}{3}}\times 16^{\frac{1}{4}}\times 9^{\frac{-1}{2}}}$$

Calculate 512 to the power of -\frac{1}{3} and get \frac{1}{8}.

$$\frac{\frac{1}{4}}{\frac{1}{8}\times 16^{\frac{1}{4}}\times 9^{\frac{-1}{2}}}$$

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

$$\frac{\frac{1}{4}}{\frac{1}{8}\times 2\times 9^{\frac{-1}{2}}}$$

Multiply \frac{1}{8} and 2 to get \frac{1}{4}.

$$\frac{\frac{1}{4}}{\frac{1}{4}\times 9^{\frac{-1}{2}}}$$

Fraction \frac{-1}{2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

$$\frac{\frac{1}{4}}{\frac{1}{4}\times 9^{-\frac{1}{2}}}$$

Calculate 9 to the power of -\frac{1}{2} and get \frac{1}{3}.

$$\frac{\frac{1}{4}}{\frac{1}{4}\times \frac{1}{3}}$$

Multiply \frac{1}{4} and \frac{1}{3} to get \frac{1}{12}.

$$\frac{\frac{1}{4}}{\frac{1}{12}}$$

Divide \frac{1}{4} by \frac{1}{12} by multiplying \frac{1}{4} by the reciprocal of \frac{1}{12}.

$$\frac{1}{4}\times 12$$

Multiply \frac{1}{4} and 12 to get 3.

$$3$$

Factor

$$3$$