Answer:
Proved
Step-by-step explanation:
Given
[tex](2 * 10^2) * (3 * 10^5) = 3.5 * 10^7 + 2.5 * 10^7[/tex]
Required
Prove
On the right hand side, we have:
[tex]2 * 10^2 * 3 * 10^5 = 3.5 * 10^7 + 2.5 * 10^7[/tex]
Rewrite:
[tex]2 * 3* 10^2 * 10^5 = 3.5 * 10^7 + 2.5 * 10^7[/tex]
[tex]6* 10^2 * 10^5 = 3.5 * 10^7 + 2.5 * 10^7[/tex]
Apply law of indices
[tex]6* 10^{2+5} = 3.5 * 10^7 + 2.5 * 10^7[/tex]
[tex]6* 10^7 = 3.5 * 10^7 + 2.5 * 10^7[/tex]
Express 6 as 3.5 + 2.5
[tex](3.5 + 2.5)* 10^7 = 3.5 * 10^7 + 2.5 * 10^7[/tex]
Open bracket
[tex]3.5 *10^7+ 2.5*10^7 = 3.5 * 10^7 + 2.5 * 10^7[/tex]
Proved
