Step 1

Given exponential expression \(\displaystyle{10}^{{{\frac{{{3}}}{{{2}}}}}}\)

By using

\(\displaystyle{a}^{{-{m}}}={\frac{{{1}}}{{{a}^{{{m}}}}}}\)

\(\displaystyle{a}^{{{m}{n}}}={\left({a}^{{{m}}}\right)}^{{{n}}}\)

Step 2

Calculation:

\(\displaystyle{10}^{{{\frac{{{3}}}{{{2}}}}}}={\frac{{{1}}}{{{10}^{{{\frac{{{3}}}{{{2}}}}}}}}}\)

\(\displaystyle={\frac{{{1}}}{{{\left({10}^{{{\frac{{{1}}}{{{2}}}}}}\right)}^{{{3}}}}}}\)

\(\displaystyle={\frac{{{1}}}{{{\left(\sqrt{{{10}}}\right)}^{{{3}}}}}}\)

\(\displaystyle={\frac{{{1}}}{{{\left(\sqrt{{{10}}}\right)}^{{{2}}}\times\sqrt{{{10}}}}}}\)

\(\displaystyle={\frac{{{1}}}{{{10}\sqrt{{{10}}}}}}\)

Given exponential expression \(\displaystyle{10}^{{{\frac{{{3}}}{{{2}}}}}}\)

By using

\(\displaystyle{a}^{{-{m}}}={\frac{{{1}}}{{{a}^{{{m}}}}}}\)

\(\displaystyle{a}^{{{m}{n}}}={\left({a}^{{{m}}}\right)}^{{{n}}}\)

Step 2

Calculation:

\(\displaystyle{10}^{{{\frac{{{3}}}{{{2}}}}}}={\frac{{{1}}}{{{10}^{{{\frac{{{3}}}{{{2}}}}}}}}}\)

\(\displaystyle={\frac{{{1}}}{{{\left({10}^{{{\frac{{{1}}}{{{2}}}}}}\right)}^{{{3}}}}}}\)

\(\displaystyle={\frac{{{1}}}{{{\left(\sqrt{{{10}}}\right)}^{{{3}}}}}}\)

\(\displaystyle={\frac{{{1}}}{{{\left(\sqrt{{{10}}}\right)}^{{{2}}}\times\sqrt{{{10}}}}}}\)

\(\displaystyle={\frac{{{1}}}{{{10}\sqrt{{{10}}}}}}\)