Question

# Using exponents, write down the radical expression, then write them down as an exponential expression using radicals 10^{-3/2}ZSK

Using exponents, write down the radical expression, then write them down as an exponential expression using radicals.
$$\displaystyle{10}^{{-\frac{{3}}{{2}}}}$$

2021-07-30
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:
$$\displaystyle{10}^{{{\frac{{{3}}}{{{2}}}}}}={\frac{{{1}}}{{{10}^{{{\frac{{{3}}}{{{2}}}}}}}}}$$
$$\displaystyle={\frac{{{1}}}{{{\left({10}^{{{\frac{{{1}}}{{{2}}}}}}\right)}^{{{3}}}}}}$$
$$\displaystyle={\frac{{{1}}}{{{\left(\sqrt{{{10}}}\right)}^{{{3}}}}}}$$
$$\displaystyle={\frac{{{1}}}{{{\left(\sqrt{{{10}}}\right)}^{{{2}}}\times\sqrt{{{10}}}}}}$$
$$\displaystyle={\frac{{{1}}}{{{10}\sqrt{{{10}}}}}}$$