Now I start to get shaky. I add the exponents, right? Which would give:

Actually, the sum of

and

is

, so the simplification should be:

. . . . .
Since

then....

Actually:

. . . . .
...so the previous expression simplifies as

. However, since the square is never negative, the absolute-value bars aren't needed, and you end up with your final result.

I make the big deal about the absolute-value bars because you could be given a "simplification" exercise along these lines where the parity (oddness or evenness) of the exponent and / or the radical

*will* matter. Keep an eye out on your next test; it's often a trick question on exams.