What is sqrt(\sqrt[4]{\sqrt[6]{\sqrt[3]{11)}}} ?

The solution to sqrt(\sqrt[4]{\sqrt[6]{\sqrt[3]{11)}}} is \sqrt[144]{11}

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simplify sqrt(\sqrt[4]{\sqrt[6]{\sqrt[3]{11)}}}

simplify

Decimal Notation

1.01679 \dots

Solution steps

Apply radical rule:

Apply exponent rule:

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

\frac{1}{4} \cdot \frac{1}{2} = \frac{1}{8}

Apply radical rule:

= (1 1^{\frac{1}{18}})^{\frac{1}{8}}

Apply exponent rule:

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

= 1 1^{\frac{1}{18} \cdot \frac{1}{8}}

\frac{1}{18} \cdot \frac{1}{8} = \frac{1}{144}

= 1 1^{\frac{1}{144}}

(1 \cdot 1 0^{- 2}) \cdot 2.5

2.55 \cdot 1 0^{- 3}

3500 (1 + 0.01735)^{- 2 \cdot 2}

4.16 \cdot 1 0^{- 5}

9. 1^{9} \cdot 7. 1^{- 2}

What is sqrt(\sqrt[4]{\sqrt[6]{\sqrt[3]{11)}}} ?
The solution to sqrt(\sqrt[4]{\sqrt[6]{\sqrt[3]{11)}}} is \sqrt[144]{11}