Solve for: 10^{-(1)/(3)} * 25^{(2)/(3)}/2^{(5)/(3)}

Expression: ${10}^{-\frac{ 1 }{ 3 }} \times {25}^{\frac{ 2 }{ 3 }}\div{2}^{\frac{ 5 }{ 3 }}$

Write the division as a fraction

$\frac{ {10}^{-\frac{ 1 }{ 3 }} \times {25}^{\frac{ 2 }{ 3 }} }{ {2}^{\frac{ 5 }{ 3 }} }$

If a negative exponent is in the numerator, move the expression to the denominator and make the exponent positive

$\frac{ {25}^{\frac{ 2 }{ 3 }} }{ {2}^{\frac{ 5 }{ 3 }} \times {10}^{\frac{ 1 }{ 3 }} }$

Use ${a}^{\frac{ m }{ n }}=\sqrt[n]{{a}^{m}}$ to transform the expression

$\frac{ {25}^{\frac{ 2 }{ 3 }} }{ \sqrt[3]{{2}^{5}} \times {10}^{\frac{ 1 }{ 3 }} }$

Use ${a}^{\frac{ m }{ n }}=\sqrt[n]{{a}^{m}}$ to transform the expression

$\frac{ \sqrt[3]{{25}^{2}} }{ \sqrt[3]{{2}^{5}} \times {10}^{\frac{ 1 }{ 3 }} }$

Use ${a}^{\frac{ m }{ n }}=\sqrt[n]{{a}^{m}}$ to transform the expression

$\frac{ \sqrt[3]{{25}^{2}} }{ \sqrt[3]{{2}^{5}}\sqrt[3]{10} }$

Evaluate the power

$\frac{ \sqrt[3]{625} }{ \sqrt[3]{{2}^{5}}\sqrt[3]{10} }$

The product of roots with the same index is equal to the root of the product

$\frac{ \sqrt[3]{625} }{ \sqrt[3]{{2}^{5} \times 10} }$

Simplify the radical expression

$\frac{ \sqrt[3]{625} }{ 2\sqrt[3]{{2}^{2} \times 10} }$

Evaluate the power

$\frac{ \sqrt[3]{625} }{ 2\sqrt[3]{4 \times 10} }$

Multiply the numbers

$\frac{ \sqrt[3]{625} }{ 2\sqrt[3]{40} }$

Simplify the radical expression

$\frac{ \sqrt[3]{625} }{ 4\sqrt[3]{5} }$

Simplify the expression

$\frac{ \sqrt[3]{125} }{ 4 }$

Evaluate the cube root

$\begin{align*}&\frac{ 5 }{ 4 } \\&\begin{array} { l }1 \frac{ 1 }{ 4 },& 1.25\end{array}\end{align*}$