Question

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

Rational exponents and radicals
ANSWERED
asked 2021-01-22
Use rational exponents to write a single radical expression.
\(\displaystyle{\sqrt[{{7}}]{{11}}}\times{\sqrt[{{6}}]{{13}}}\)

Expert Answers (1)

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 \(\displaystyle{\sqrt[{{42}}]{{{1771561}\times{62748517}}}}\)
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