Solve {l}{sqrt[3]{[(16)^-3/4*(125)^-2]}}{sqrt[3]{[(16)^-3/4*(125)^-2]}}

$$\left. \begin{array} { l } { \sqrt[ 3 ] { [ ( 16 ) ^ { - 3 / 4 } \times ( 125 ) ^ { - 2 } ] } } \\ { \sqrt[ 3 ] { [ ( 16 ) ^ { - 3 / 4 } \times ( 125 ) ^ { - 2 } ] } } \end{array} \right.$$

Sort

$$\frac{1}{50},\ \frac{1}{50}$$

Solution Steps

Calculate 16 to the power of -\frac{3}{4} and get \frac{1}{8}.

$$sort(\sqrt[3]{\frac{1}{8}\times 125^{-2}},\sqrt[3]{16^{-\frac{3}{4}}\times 125^{-2}})$$

Calculate 125 to the power of -2 and get \frac{1}{15625}.

$$sort(\sqrt[3]{\frac{1}{8}\times \frac{1}{15625}},\sqrt[3]{16^{-\frac{3}{4}}\times 125^{-2}})$$

Multiply \frac{1}{8} and \frac{1}{15625} to get \frac{1}{125000}.

$$sort(\sqrt[3]{\frac{1}{125000}},\sqrt[3]{16^{-\frac{3}{4}}\times 125^{-2}})$$

Calculate \sqrt[3]{\frac{1}{125000}} and get \frac{1}{50}.

$$sort(\frac{1}{50},\sqrt[3]{16^{-\frac{3}{4}}\times 125^{-2}})$$

Calculate 16 to the power of -\frac{3}{4} and get \frac{1}{8}.

$$sort(\frac{1}{50},\sqrt[3]{\frac{1}{8}\times 125^{-2}})$$

Calculate 125 to the power of -2 and get \frac{1}{15625}.

$$sort(\frac{1}{50},\sqrt[3]{\frac{1}{8}\times \frac{1}{15625}})$$

Multiply \frac{1}{8} and \frac{1}{15625} to get \frac{1}{125000}.

$$sort(\frac{1}{50},\sqrt[3]{\frac{1}{125000}})$$

Calculate \sqrt[3]{\frac{1}{125000}} and get \frac{1}{50}.

$$sort(\frac{1}{50},\frac{1}{50})$$

The list values are already in order.

$$\frac{1}{50},\frac{1}{50}$$

Evaluate

$$\frac{1}{50},\ \frac{1}{50}$$