What is \sqrt[\sqrt[3]{6}]{2^{36}} ?

The solution to \sqrt[\sqrt[3]{6}]{2^{36}} is 64^{6^{2/3}}

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simplify \sqrt[\sqrt[3]{6}]{2^{36}}

simplify

6 4^{6^{\frac{2}{3}}}

Decimal Notation

920184.41305 \dots

Solution steps

Apply radical rule:

Apply exponent rule:

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

= 2^{6 \cdot 6^{\frac{2}{3}}}

Apply exponent rule:

a^{b x} = (a^{b})^{x}

2^{6 \cdot 6^{\frac{2}{3}}} = (2^{6})^{6^{\frac{2}{3}}}

= (2^{6})^{6^{\frac{2}{3}}}

2^{6} = 64

= 6 4^{6^{\frac{2}{3}}}

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What is \sqrt[\sqrt[3]{6}]{2^{36}} ?
The solution to \sqrt[\sqrt[3]{6}]{2^{36}} is 64^{6^{2/3}}