Question

Rewrite n sqrt x^m using rational expression.

Answer 1

We are given expression $\sqrt[n]{x^m}$.

We need to convert it in rational exponent expression.

We know the rule for rational exponent expression as following:

$\sqrt[b]{a^c} = a^{\frac{c}{b}}$.

If we compare given radical expression, x is a and it's nth radical.

Therefore, b = n and exponent of x is m. Therefore, m = c.

Therefore, $\sqrt[n]{x^m}$ can be written as  $x^{\frac{m}{n}}$.