Question

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

Answer 1

$100^a \time 1000^b = 10^{2a} \times 10^{3b} = 10^{2a + 3b}$

$10^{w} = 10^{2a + 3b}$

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