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

The solution to sqrt(\sqrt{\sqrt{\sqrt{x)}}} is \sqrt[16]{x}

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simplify sqrt(\sqrt{\sqrt{\sqrt{x)}}}

simplify

x

Solution steps

x

Apply radical rule:

= (x^{\frac{1}{8}})^{\frac{1}{2}}

Apply exponent rule:

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

assuming

a \geq 0

= x^{\frac{1}{8} \cdot \frac{1}{2}}

\frac{1}{8} \cdot \frac{1}{2} = \frac{1}{16}

= x^{\frac{1}{16}}

e^{- l n (x - 1)}

e^{- c}

What is sqrt(\sqrt{\sqrt{\sqrt{x)}}} ?
The solution to sqrt(\sqrt{\sqrt{\sqrt{x)}}} is \sqrt[16]{x}