What is \sqrt[3]{\sqrt[5]{a}} ?

The solution to \sqrt[3]{\sqrt[5]{a}} is \sqrt[15]{a}

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simplify \sqrt[3]{\sqrt[5]{a}}

simplify

Solution steps

Apply radical rule:

= (a^{\frac{1}{5}})^{\frac{1}{3}}

Apply exponent rule:

(a^{b})^{c} = a^{b c},

assuming

a \geq 0

= a^{\frac{1}{5} \cdot \frac{1}{3}}

\frac{1}{5} \cdot \frac{1}{3} = \frac{1}{15}

= a^{\frac{1}{15}}

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What is \sqrt[3]{\sqrt[5]{a}} ?
The solution to \sqrt[3]{\sqrt[5]{a}} is \sqrt[15]{a}