2004 #04 and 38

How well do yours remember exponents?

Difficulty: Simple, maybe.

Difficulty: Number theory. Tough little bastard until the AHA! moment.

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest 2004

answer 04, answer 38.