The rational exponent expression of \(\sqrt[5]{7n}\) will be \((7n)^\frac{1}{5}\) .
What is rational exponent ?
Rational exponent are exponents of numbers that are expressed as rational numbers, that is, in \(a^{\frac{p}{q} }\) form.
i.e. \(a^{\frac{p}{q} }=\sqrt[q]{a^n}\)
We have,
\(\sqrt[5]{7n}\)
so, Using the mentioned formula,
\(a^{\frac{p}{q} }=\sqrt[q]{a^n}\)
\(\sqrt[5]{7n}=(7n)^\frac{1}{5}\)
So, this is the rational expression \((7n)^\frac{1}{5}\) using above mentioned formula.
Hence, we can say that the rational exponent expression of \(\sqrt[5]{7n}\) will be \((7n)^\frac{1}{5}\) .
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