What is \sqrt[5]{\sqrt[6]{32x^5}} ?

The solution to \sqrt[5]{\sqrt[6]{32x^5}} is \sqrt[6]{2}\sqrt[30]{x^5}

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simplify \sqrt[5]{\sqrt[6]{32x^5}}

simplify

Solution steps

Apply radical rule:

= ((32 x^{5})^{\frac{1}{6}})^{\frac{1}{5}}

Apply exponent rule:

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

assuming

a \geq 0

= (32 x^{5})^{\frac{1}{6} \cdot \frac{1}{5}}

\frac{1}{6} \cdot \frac{1}{5} = \frac{1}{30}

= (32 x^{5})^{\frac{1}{30}}

Apply radical rule:

assuming

a \geq 0, b \geq 0

8.4 \cdot 1 0^{- 6}

- e^{- \frac{2 ( 1 )}{5}}

5.31 \cdot 1 0^{- 5}

25

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What is \sqrt[5]{\sqrt[6]{32x^5}} ?
The solution to \sqrt[5]{\sqrt[6]{32x^5}} is \sqrt[6]{2}\sqrt[30]{x^5}