This is probably an easy question, but I'm not able to figure it out.

Are the following the same:

Field of fractions of the ring of Witt vectors over the algebraic closure of $\mathbb{F}_p$

Algebraic closure of the field of p-adics (which is the field of fractions of the ring of Witt vectors over $\mathbb{F}_p$)

In other words, does the operation of taking the field of fractions of the ring of Witt vectors commute with the operation of taking the algebraic closure?