Question

write the following as a radical expression.
$5^{\frac{6}{7}}$

Explanation:

Step1: Recall the exponent to radical rule

The rule for converting an exponent \(a^{\frac{m}{n}}\) to a radical is \(a^{\frac{m}{n}}=\sqrt[n]{a^{m}}\) (where \(n\) is the index of the radical and \(m\) is the power of the base inside the radical).
For the expression \(5^{\frac{6}{7}}\), here \(a = 5\), \(m=6\) and \(n = 7\).

Step2: Apply the rule

Using the rule \(a^{\frac{m}{n}}=\sqrt[n]{a^{m}}\), substitute \(a = 5\), \(m = 6\) and \(n=7\) into the formula. We get \(\sqrt[7]{5^{6}}\).

Answer:

\(\sqrt[7]{5^{6}}\)