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

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

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

simplify

Solution steps

Apply radical rule:

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

Apply exponent rule:

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

assuming

a \geq 0

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

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

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

(14)^{3}

(e^{1})^{2}

\frac{( \frac{3}{4} ) ^{6}}{( \frac{3}{4} ) ^{- 6}}

0.5 e^{- 0.5}

(2)^{11}

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