Given problem: [tex]\frac{8*10^{-4}}{2*10^2}[/tex].
Solution: We can see that first we have 8 and 2 numbers in front of 10's powers.
So, we need to simplify 8 over 2 first.
If we divide 8 by 2, we get 4.
Now, let us work on 10's and their powers.
[tex]10^{-4}[/tex] is being divided by [tex]10^{2}.[/tex]
We can apply quotient rule of exponents remaining part.
According to quotient rule of exponents, [tex]\frac{a^m}{a^n}=a^{m-n}[/tex]
If we apply same rule, we need to subtract exponents of 10's.
[tex]\frac{10^{-4}}{10^2}=10^{-4-(-2)}[/tex]
If we simplify exponent part -4-(-2), it will give us -4+2 =-2.
So, [tex]10^{-4-(-2)}=10^{-2}[/tex]
And final answer would be [tex]4 \times 10^{-2}[/tex].
