Answer:
3rd choice
Step-by-step explanation:
In division for variables with same base, you do subtract top exponent minus bottom exponent. She did that correctly since -3-(-1)=-3+1=-2 and -2-1=-3.
The problem said m=-2 and n=4 and she replace m with (-2) and n with (4). She did this correctly.
You can multiply base numbers unless the exponents are the same 4 doesn't have the exponent -2 on it so you can't do (4(-2))^(-2)
The error is the 3rd option.
We start with
[tex]\dfrac{4m^{-3}n^{-2}}{m^{-1}n}[/tex]
Simplifying the exponents, we have
[tex]\dfrac{4m^{-3}n^{-2}}{m^{-1}n} = 4m^{-3}n^{-2} (mn^{-1}) = 4m^{-3+1}n^{-2-1}=4m^{-2}n^{-3}[/tex]
So, the exponents are ok.
If we plug the values, we have
[tex]4m^{-2}n^{-3} \mapsto 4(-2)^{-2}(4)^{-3} = 4\cdot \dfrac{1}{(-2)^2}\cdot\dfrac{1}{4^3} = 4\cdot \dfrac{1}{4}\cdot \dfrac{1}{64} = \dfrac{1}{64}[/tex]
So, she didn't apply the exponent -2 correctly.
