# Use rational exponents to write a single radical expression. displaystyle{sqrt[{{7}}]{{11}}}times{sqrt[{{6}}]{{13}}}

Question
Use rational exponents to write a single radical expression.
$$\displaystyle{\sqrt[{{7}}]{{11}}}\times{\sqrt[{{6}}]{{13}}}$$

2021-01-23
Step 1
Given:
$$\displaystyle{\sqrt[{{7}}]{{11}}}\times{\sqrt[{{6}}]{{13}}}$$
$$\displaystyle{11}^{{\frac{1}{{7}}}}\times{13}^{{\frac{1}{{6}}}}$$
$$\displaystyle{11}^{{\frac{6}{{42}}}}\times{13}^{{\frac{7}{{42}}}}$$
$$\displaystyle{\sqrt[{{42}}]{{{11}^{6}\times{13}^{7}}}}$$
Step 2
Therefore, answer is $$\displaystyle{\sqrt[{{42}}]{{{1771561}\times{62748517}}}}$$

### Relevant Questions

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To simplify:
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$$\frac{Radical\ expression\ Exponential\ expression}{\sqrt[5]{5^{3}}}$$
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