Since I used properties of exponents here to simplify the expression, but since the definition of a fractional exponent is new to a friend, how would I apply the definition to this problem?

100^-3/2

=(10²)^-3/2

=10^2*(-3/2) [since, (a^b)^c=a^b*c]

=10^-3

=1/10³ [since, a^-b=1/a^b]

=1/1000