Nested Square Roots

Question

Question:

Solve for $\sqrt{x\sqrt{x\sqrt{x}}}$

I know this may be a duplicate but I have not found one yet.

Additionally I understand the logic for base 8 but why would the answer be

$x^\frac 78$

Instead of

$x^\frac 18$

Answer 1

Hint:

Use the following two facts:

1. $\sqrt{ab}=\sqrt{a}\sqrt{b}$
2. $\sqrt{\sqrt{a}} = \sqrt{a^\frac12} = \left(a^\frac12\right)^\frac12 = a^{\frac12\cdot\frac12} = a^\frac14$