Solve {l}{(0.000008)^{-2/3}*(0.008)^{2}*30^-2}{(0.0256)^-frac{1{2}}*(0.125)^frac{1{3}}*(0.3)^2}

$$\left. \begin{array} { l } { ( 0.000008 ) ^ { - \frac { 2 } { 3 } } \times ( 0.008 ) ^ { 2 } \times 30 ^ { - 2 } } \\ { ( 0.0256 ) ^ { - \frac { 1 } { 2 } } \times ( 0.125 ) ^ { \frac { 1 } { 3 } } \times ( 0.3 ) ^ { 2 } } \end{array} \right.$$

Sort

$$\frac{1}{5625},\ 0.28125$$

Solution Steps

Calculate 0.000008 to the power of -\frac{2}{3} and get 2500.

$$sort(2500\times 0.008^{2}\times 30^{-2},0.0256^{-\frac{1}{2}}\times 0.125^{\frac{1}{3}}\times 0.3^{2})$$

Calculate 0.008 to the power of 2 and get 0.000064.

$$sort(2500\times 0.000064\times 30^{-2},0.0256^{-\frac{1}{2}}\times 0.125^{\frac{1}{3}}\times 0.3^{2})$$

Multiply 2500 and 0.000064 to get 0.16.

$$sort(0.16\times 30^{-2},0.0256^{-\frac{1}{2}}\times 0.125^{\frac{1}{3}}\times 0.3^{2})$$

Calculate 30 to the power of -2 and get \frac{1}{900}.

$$sort(0.16\times \frac{1}{900},0.0256^{-\frac{1}{2}}\times 0.125^{\frac{1}{3}}\times 0.3^{2})$$

Multiply 0.16 and \frac{1}{900} to get \frac{1}{5625}.

$$sort(\frac{1}{5625},0.0256^{-\frac{1}{2}}\times 0.125^{\frac{1}{3}}\times 0.3^{2})$$

Calculate 0.0256 to the power of -\frac{1}{2} and get \frac{25}{4}.

$$sort(\frac{1}{5625},\frac{25}{4}\times 0.125^{\frac{1}{3}}\times 0.3^{2})$$

Calculate 0.125 to the power of \frac{1}{3} and get \frac{1}{2}.

$$sort(\frac{1}{5625},\frac{25}{4}\times \frac{1}{2}\times 0.3^{2})$$

Multiply \frac{25}{4} and \frac{1}{2} to get \frac{25}{8}.

$$sort(\frac{1}{5625},\frac{25}{8}\times 0.3^{2})$$

Calculate 0.3 to the power of 2 and get 0.09.

$$sort(\frac{1}{5625},\frac{25}{8}\times 0.09)$$

Multiply \frac{25}{8} and 0.09 to get \frac{9}{32}.

$$sort(\frac{1}{5625},\frac{9}{32})$$

Least common denominator of the numbers in the list \frac{1}{5625},\frac{9}{32} is 180000. Convert numbers in the list to fractions with denominator 180000.

$$\frac{32}{180000},\frac{50625}{180000}$$

Evaluate

$$\frac{1}{5625},\ 0.28125$$