Solve (25^{frac{1/2}}{16^{-1/2}})*(2^-3/81^frac{1{2}})div(frac{125^frac{1{3}}}{27^frac{1{3}}})

$$( \frac { 25 ^ { \frac { 1 } { 2 } } } { 16 ^ { - \frac { 1 } { 2 } } } ) \times ( \frac { 2 ^ { - 3 } } { 81 ^ { \frac { 1 } { 2 } } } ) \div ( \frac { 125 ^ { \frac { 1 } { 3 } } } { 27 ^ { \frac { 1 } { 3 } } } )$$

Evaluate

$$\frac{1}{6}\approx 0.166666667$$

Solution Steps

Calculate 25 to the power of \frac{1}{2} and get 5.

$$\frac{\frac{5}{16^{-\frac{1}{2}}}\times \frac{2^{-3}}{81^{\frac{1}{2}}}}{\frac{125^{\frac{1}{3}}}{27^{\frac{1}{3}}}}$$

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

$$\frac{\frac{5}{\frac{1}{4}}\times \frac{2^{-3}}{81^{\frac{1}{2}}}}{\frac{125^{\frac{1}{3}}}{27^{\frac{1}{3}}}}$$

Divide 5 by \frac{1}{4} by multiplying 5 by the reciprocal of \frac{1}{4}.

$$\frac{5\times 4\times \frac{2^{-3}}{81^{\frac{1}{2}}}}{\frac{125^{\frac{1}{3}}}{27^{\frac{1}{3}}}}$$

Multiply 5 and 4 to get 20.

$$\frac{20\times \frac{2^{-3}}{81^{\frac{1}{2}}}}{\frac{125^{\frac{1}{3}}}{27^{\frac{1}{3}}}}$$

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

$$\frac{20\times \frac{\frac{1}{8}}{81^{\frac{1}{2}}}}{\frac{125^{\frac{1}{3}}}{27^{\frac{1}{3}}}}$$

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

$$\frac{20\times \frac{\frac{1}{8}}{9}}{\frac{125^{\frac{1}{3}}}{27^{\frac{1}{3}}}}$$

Express \frac{\frac{1}{8}}{9} as a single fraction.

$$\frac{20\times \frac{1}{8\times 9}}{\frac{125^{\frac{1}{3}}}{27^{\frac{1}{3}}}}$$

Multiply 8 and 9 to get 72.

$$\frac{20\times \frac{1}{72}}{\frac{125^{\frac{1}{3}}}{27^{\frac{1}{3}}}}$$

Multiply 20 and \frac{1}{72} to get \frac{5}{18}.

$$\frac{\frac{5}{18}}{\frac{125^{\frac{1}{3}}}{27^{\frac{1}{3}}}}$$

Calculate 125 to the power of \frac{1}{3} and get 5.

$$\frac{\frac{5}{18}}{\frac{5}{27^{\frac{1}{3}}}}$$

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

$$\frac{\frac{5}{18}}{\frac{5}{3}}$$

Divide \frac{5}{18} by \frac{5}{3} by multiplying \frac{5}{18} by the reciprocal of \frac{5}{3}.

$$\frac{5}{18}\times \frac{3}{5}$$

Multiply \frac{5}{18} and \frac{3}{5} to get \frac{1}{6}.

$$\frac{1}{6}$$

Factor

$$\frac{1}{2 \cdot 3} = 0.16666666666666666$$