${2}^{-\frac{ 31 }{ 10 }}$
Express with a positive exponent using ${a}^{-n}=\frac{ 1 }{ {a}^{n} }$$\frac{ 1 }{ {2}^{\frac{ 31 }{ 10 }} }$
Use ${a}^{\frac{ m }{ n }}=\sqrt[n]{{a}^{m}}$ to transform the expression$\frac{ 1 }{ \sqrt[10]{{2}^{31}} }$
Simplify the radical expression$\frac{ 1 }{ {2}^{3}\sqrt[10]{2} }$
Evaluate the power$\frac{ 1 }{ 8\sqrt[10]{2} }$
Rationalize the denominator$\frac{ \sqrt[10]{{2}^{9}} }{ 16 }$
Evaluate the power$\begin{align*}&\frac{ \sqrt[10]{512} }{ 16 } \\&\approx0.116629\end{align*}$