Use rational exponents to write a single radical expression.

necessaryh 2021-09-08 Answered

Use rational exponents to write a single radical expression.
\(\sqrt[3]{3}\sqrt{3}\)

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Expert Answer

Sally Cresswell
Answered 2021-09-09 Author has 4161 answers

Given expression by y:
\(\displaystyle{y}=\sqrt[3]{3}\sqrt{3}\)
\(\displaystyle{y}={\left({3}\sqrt{{{3}}}\right)}^{{\frac{{{1}}}{{{3}}}}}\)
\(\displaystyle{y}={\left[{3}^{{1}}\times{3}^{{\frac{{{1}}}{{{2}}}}}\right]}^{{\frac{{{1}}}{{{3}}}}}\)
\(\displaystyle{y}={\left[{3}^{{{\left({1}+{\frac{{{1}}}{{{2}}}}\right)}}}\right]}^{{\frac{{{1}}}{{{3}}}}}\)
\(\displaystyle{y}={\left[{3}^{{{\frac{{{2}+{1}}}{{{2}}}}}}\right]}^{{\frac{{{1}}}{{{3}}}}}\)
\(\displaystyle{y}={\left[{3}^{{\frac{{{1}}}{{{2}}}}}\right]}^{{\frac{{{1}}}{{{3}}}}}\)
\(\displaystyle{3}^{{{\frac{{{3}}}{{{2}}}}\times{\frac{{{1}}}{{{3}}}}}}\)
\(\displaystyle{y}={3}^{{\frac{{{1}}}{{{2}}}}}\)
\(\displaystyle=\sqrt{{{3}}}\)
Hence,
\(\sqrt[3]{3}\sqrt{3}=\sqrt{{{3}}}\)

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