Evaluate: 2^{-3.1}

Expression: ${2}^{-3.1}$

Convert the decimal into a fraction

${2}^{-\frac{ 31 }{ 10 }}$

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

$\begin{align*}&\frac{ \sqrt[10]{512} }{ 16 } \\&\approx0.116629\end{align*}$