Question

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

Rational exponents and radicals
ANSWERED
asked 2021-07-29
Using exponents, write down the radical expression, then write them down as an exponential expression using radicals.
\(\displaystyle{10}^{{-\frac{{3}}{{2}}}}\)

Expert Answers (1)

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