# Write the radical expression using exponents and each exponential expression usi

Write the radical expression using exponents and each exponential expression using radicals.
$$\displaystyle{10}^{{-\frac{{3}}{{2}}}}$$

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davonliefI
Given exponential expression $$\displaystyle{10}^{{-{\frac{{{3}}}{{{2}}}}}}$$
By using
$$\displaystyle{a}^{{-{m}}}={\frac{{{1}}}{{{a}^{{m}}}}}$$
$$\displaystyle{a}^{{{m}{n}}}={\left({a}^{{m}}\right)}^{{n}}$$
Thus,
$$\displaystyle{10}^{{-{\frac{{{3}}}{{{2}}}}}}={\frac{{{1}}}{{{10}^{{{\frac{{{3}}}{{{2}}}}}}}}}$$
$$\displaystyle={\frac{{{1}}}{{{\left({10}^{{{\frac{{{1}}}{{{2}}}}}}\right)}^{{3}}}}}$$
$$\displaystyle={\frac{{{1}}}{{{\left(\sqrt{{{10}}}\right)}^{{3}}}}}$$
$$\displaystyle={\frac{{{1}}}{{{\left(\sqrt{{{10}}}\right)}^{{2}}\times\sqrt{{{10}}}}}}$$
$$\displaystyle={\frac{{{1}}}{{{10}\sqrt{{{10}}}}}}$$