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)}`