100a×1000b can be written in the form 10w. show that w=2a+3b

100^a x 1000^b
=(10^2)^a x (10^3)^b
By the laws of exponents, (x^a)^b = x^ab
=(10^2a) x (10^3b)
Also, since x^a * x^b = x^(a+b)
=10^(2a+3b)
If this is in the form 10^w,
w = 2a+3b

The correct answer is: 2