Question

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

Answer 1

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

Answer 2

It is proved that
`w=2a+3b`

Explanation:

It is given that
`100^a* 1000^b` can be written in the form
`10^w`

It means

`100^a* 1000^b=10^w`

`(10^2)^a* (10^3)^b=10^w`

`10^(2a)* {10^3b}=10^w`
`[\because (a^m)^n=a^(mn])`

`10^(2a+3b)=10^w`
`[\because a^m* a^n=a^(m+n)]`

Base is same on both the sides. On comparing the powers we get,

`2a+3b=w`

Hence proved.