Question

100^a x 1000^b can be written in the form 10^w

Show that w = 2a + 3b

Answer 1

`100^a \time 1000^b = 10^(2a) * 10^(3b) = 10^(2a + 3b)`


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


`w = 2a + 3b \text { (shown)}`