Calculate: 12^{-(2)/(3)}

Expression: ${12}^{-\frac{ 2 }{ 3 }}$

Express with a positive exponent using ${a}^{-n}=\frac{ 1 }{ {a}^{n} }$

$\frac{ 1 }{ {12}^{\frac{ 2 }{ 3 }} }$

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

$\frac{ 1 }{ \sqrt[3]{{12}^{2}} }$

Multiply the fraction by $\frac{ \sqrt[3]{12} }{ \sqrt[3]{12} }$

$\frac{ 1 }{ \sqrt[3]{{12}^{2}} } \times \frac{ \sqrt[3]{12} }{ \sqrt[3]{12} }$

To multiply the fractions, multiply the numerators and denominators separately

$\frac{ 1\sqrt[3]{12} }{ \sqrt[3]{{12}^{2}}\sqrt[3]{12} }$

Any expression multiplied by $1$ remains the same

$\frac{ \sqrt[3]{12} }{ \sqrt[3]{{12}^{2}}\sqrt[3]{12} }$

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

$\frac{ \sqrt[3]{12} }{ \sqrt[3]{{12}^{2} \times 12} }$

Calculate the product

$\frac{ \sqrt[3]{12} }{ \sqrt[3]{{12}^{3}} }$

Reduce the index of the radical and exponent with $3$

$\begin{align*}&\frac{ \sqrt[3]{12} }{ 12 } \\&\approx0.190786\end{align*}$