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

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

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

simplify

Solution steps

Apply radical rule:

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

Apply exponent rule:

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

assuming

a \geq 0

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

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

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

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