# Use rational exponents to write a single radical expression.

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

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Sally Cresswell

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,
$$\sqrt[3]{3}\sqrt{3}=\sqrt{{{3}}}$$