Why does lim10^(3-x) as x approaches infinity = 0?

Question

And why does lim10^(1/x) as x approaches infinity = 1?

Are properties of infinite limits involved here?

Answer 1

lim (10^(3-x)=lim 10^(-x)= lim (1/10^x) which of course is zero

by definition, anything to the zero power is 1

a^0 defined=1