What is sqrt(\sqrt[5]{3\sqrt[3]{3\sqrt{3)}}} ?

The solution to sqrt(\sqrt[5]{3\sqrt[3]{3\sqrt{3)}}} is 3^{3/20}

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simplify sqrt(\sqrt[5]{3\sqrt[3]{3\sqrt{3)}}}

simplify

3^{\frac{3}{20}}

Decimal Notation

1.17914 \dots

Solution steps

Apply radical rule:

Apply exponent rule:

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

\frac{1}{5} \cdot \frac{1}{2} = \frac{1}{10}

Apply radical rule:

assuming

a \geq 0, b \geq 0

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

= 3^{\frac{1}{10} + \frac{1}{20}}

Join

\frac{1}{10} + \frac{1}{20} : \frac{3}{20}

= 3^{\frac{3}{20}}

1 0^{- 5 x^{x}} e^{- x^{2}}

e^{- t} \cdot (- 3) e^{- 3 t}

(x + h)^{2} x^{2}

\frac{13}{14}

What is sqrt(\sqrt[5]{3\sqrt[3]{3\sqrt{3)}}} ?
The solution to sqrt(\sqrt[5]{3\sqrt[3]{3\sqrt{3)}}} is 3^{3/20}