5^4/25
= (5^4)/(5^2)
The quotient of powers allows you to subtract exponents when dividing by powers of the same base:
= 5 ^ (4-2)
=5 ^ 2
= 25
I'm not sure I fully understand what the teacher is after in the second and third questions, but you can move a numerator to a denominator by inverting it (1 / x), which is the same as taking it to the power of -1:
1 / ((5 ^ -4) x (5 ^ 2))
= 1 / (5 ^ (-4 + 2))
= 1 / 5 ^ -2
And the same reasoning applies to taking a denominator back to the numerator, viz changing the sign of the exponent:
= 5 ^ 2 = 25