Let C be the curve $y=\frac{x^4}{a^2}+\frac{1}{a^{-n}}$ for $0\mathrm{.}4x2\mathrm{.}6.$ The graph follows.

Find the arc length of $C.$

First find and simplify $\sqrt[\phantom{2}]{1+y^{12}}=$

Hint: $1+y^{\text{'}2}$ should be a perfect square,

Then arc length $-$