Write with Rational (Fractional) Exponents m root of n root of a

$\sqrt[m]{\sqrt[n]{a}}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[n]{a}$ as $a^{\frac{1}{n}}$ .

$\sqrt[m]{a^{\frac{1}{n}}}$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[m]{a^{\frac{1}{n}}}$ as $a^{\frac{\frac{1}{n}}{m}}$ .

$a^{\frac{\frac{1}{n}}{m}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$a^{\frac{1}{n} \cdot \frac{1}{m}}$

Step 4

Multiply $\frac{1}{n}$ by $\frac{1}{m}$ .

$a^{\frac{1}{n m}}$