Write the radical expression using exponents and each exponential expression usi

FobelloE 2021-09-22 Answered
Write the radical expression using exponents and each exponential expression using radicals.
\(\displaystyle{10}^{{-\frac{{3}}{{2}}}}\)

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Expert Answer

davonliefI
Answered 2021-09-23 Author has 23481 answers
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,
\(\displaystyle{10}^{{-{\frac{{{3}}}{{{2}}}}}}={\frac{{{1}}}{{{10}^{{{\frac{{{3}}}{{{2}}}}}}}}}\)
\(\displaystyle={\frac{{{1}}}{{{\left({10}^{{{\frac{{{1}}}{{{2}}}}}}\right)}^{{3}}}}}\)
\(\displaystyle={\frac{{{1}}}{{{\left(\sqrt{{{10}}}\right)}^{{3}}}}}\)
\(\displaystyle={\frac{{{1}}}{{{\left(\sqrt{{{10}}}\right)}^{{2}}\times\sqrt{{{10}}}}}}\)
\(\displaystyle={\frac{{{1}}}{{{10}\sqrt{{{10}}}}}}\)
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