why do you subtract exponents when dividing powers with the same base

Question

 exponents

Answer 1

when you multiply with the same base you add the exponents

(10^3)*(10^2)=10^(3+2)=10^5

10^3=10*10*10

10^2=10*10

10^3*10^2=10*10*10*10*10=10^? how many tens are there ? 5, therefore the answer is 10^5

when you divide with the same base you subtract the exponents

10^5/10^2=10^(5-2)=10^3

1/10^2 is the same as 10^(-2)

10^5/10^2=(10^5)*(10^[-2])=10^(5+[-2])=10^3

10^5/10^2=(10*10*10*10*10)/(10*10)=?

simplify or cancel out two tens from both the numerator and the denominator

this leaves 10*10*10=10^3

10^3/10^7=10^(3-7)=10^(-4)=1/10^4

10^3/10^7=(10^3)*(10^[-7])=10^(3+[-7])=10^(-4)=1/10^4

10*10*10/10*10*10*10*10*10*10=?

simplify or cancel three tens from both the numerator and the denominator

this leaves 1/10*10*10*10=1/10^4

Hope this clears things up for you.