Answer :
Answer:
- See the law and the hypothetical example below.
Explanation:
The index law that you are dealing with is:
[tex]\dfrac{a^m}{a^n}=a^{m-n}[/tex]
It is used when you have the quotient of powers with the same base.
To show you how to use that rule, let's work an example
Simplify:
[tex]\dfrac{9a(m^2)}{6b(m^4)}[/tex]
Factor 9 as 3² and 6 as 2×3:
[tex]\dfrac{3^2a(m^2)}{2\times 3b(m^4)}[/tex]
Group the factor with equal base:
[tex]\dfrac{a}{2b}\times \dfrac{3^2}{3}\times \dfrac{m^2}{m^4}[/tex]
Use the index law:
[tex]\dfrac{a}{2b}\times {3^{(2-1)}}\times m^{(2-4)}\\\\\\ \dfrac{a}{2b}\times3\times m^{-2}\\\\\\\dfrac{3a}{2bm^2}[/tex]
Note that it was used an additional rule: [tex]a^{-n}=\dfrac{1}{a^n}[/tex]
Thus, [tex]m^{-2}=\dfrac{1}{m^2}[/tex]