What is sqrt(\sqrt{\sqrt{\sqrt{\sqrt{64)}}}} ?

The solution to sqrt(\sqrt{\sqrt{\sqrt{\sqrt{64)}}}} is \sqrt[32]{64}

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simplify sqrt(\sqrt{\sqrt{\sqrt{\sqrt{64)}}}}

simplify

64

Solution steps

64

Apply radical rule:

a = a^{\frac{1}{2}}

Apply exponent rule:

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

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

Apply radical rule:

Apply exponent rule:

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

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

Apply radical rule:

= (6 4^{\frac{1}{4}})^{\frac{1}{8}}

Apply exponent rule:

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

= 6 4^{\frac{1}{4} \cdot \frac{1}{8}}

\frac{1}{4} \cdot \frac{1}{8} = \frac{1}{32}

= 6 4^{\frac{1}{32}}

e^{- \frac{10}{24}}

8.5 \cdot 1 0^{- 3} \cdot 10

\frac{1}{2 ^{2} \cdot 1} x^{2 - 1} e^{- \frac{x}{2}}

(101083)^{(- 84)}

6.49 \cdot 1 0^{- 9}

What is sqrt(\sqrt{\sqrt{\sqrt{\sqrt{64)}}}} ?
The solution to sqrt(\sqrt{\sqrt{\sqrt{\sqrt{64)}}}} is \sqrt[32]{64}