First of all, put the value of \(\displaystyle{x}=\frac{3}{{2}}\) in \(f(x)\).

\(\displaystyle{f{{\left({x}\right)}}}={10}^{{x}}\)

\(\displaystyle{f{{\left({\frac{{{3}}}{{{2}}}}\right)}}}={10}^{{{\frac{{{3}}}{{{2}}}}}}\)

Now, use the radicals and simplify to find \(\displaystyle f{{\left(\frac{3}{{2}}\right)}}\).

\(\displaystyle{f{{\left({\frac{{{3}}}{{{2}}}}\right)}}}={10}^{{{\frac{{{3}}}{{{2}}}}}}\)

\(\sqrt[2]{10^3}\)

\(\displaystyle=\sqrt[2]{{10}\times{10}\times{10}}\)

\(\displaystyle{10}\times\sqrt[2]{10}\)

\(\displaystyle={10}\times{3.162}\)

\(\displaystyle{f{{\left({\frac{{{3}}}{{{2}}}}\right)}}}={31.62}\)