The given expression is
100^a x 1000^b
Recall,
100 = 10^2
1000 = 10^3
Thus, the expression would be
10^2a x 10^3b
We would apply one of the rules of exponents which is expressed as
a^b x a^c = a^(b + c)
By applying this rule, we have
10^(2a + 3b)
By comparing it with 10^w, we have
w = 2a + 3b