What is \sqrt[\sqrt[3]{6}]{3^{54}} ?

The solution to \sqrt[\sqrt[3]{6}]{3^{54}} is 19683^{6^{2/3}}

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simplify \sqrt[\sqrt[3]{6}]{3^{54}}

simplify

1968 3^{6^{\frac{2}{3}}}

Decimal Notation

1.50931 E 14

Solution steps

Apply radical rule:

Apply exponent rule:

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

= 3^{9 \cdot 6^{\frac{2}{3}}}

Apply exponent rule:

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

3^{9 \cdot 6^{\frac{2}{3}}} = (3^{9})^{6^{\frac{2}{3}}}

= (3^{9})^{6^{\frac{2}{3}}}

3^{9} = 19683

= 1968 3^{6^{\frac{2}{3}}}

e^{- 3} \cdot e^{x}

- e^{- a}

(42) (32)

\frac{17}{21}

- e^{- e}

What is \sqrt[\sqrt[3]{6}]{3^{54}} ?
The solution to \sqrt[\sqrt[3]{6}]{3^{54}} is 19683^{6^{2/3}}