Question

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

Answer 1

$\text{Use}\ (a^n)^m=a^{n+m}\ \text{and}\ a^n\cdot a^m=a^{n+m}.\\\\100^a=(10^2)^a=10^{2a}\\\\1000^b=(10^3)^b=10^{3b}\\\\100^a\cdot1000^b=10^{2a}\cdot10^{3b}=\boxed{10^{2a+3b}}$