Answer:
[tex]= \frac{2m^2n^8}{3}[/tex]
Step-by-step explanation:
Given expression is
[tex](\frac{4m^{-2}n^8}{9m^{-6}n^{-8}} )^{\frac{1}{2}[/tex]
The correct simplified form is shown below:-
From the above equation, we will simplify
we will shift [tex]m^{-6}[/tex] to the numerator and we will use the negative exponent rule, that is
[tex]= (\frac{4m^{-2}n^8m^6}{9n^{-8}} )^{\frac{1}{2}[/tex]
now we will shift the [tex]n^{-8}[/tex] to the numerator and we will use the negative exponent rule, that is
[tex]= (\frac{4m^{-2}n^8m^6n^8}{9} )^{\frac{1}{2}[/tex]
here we will solve the above equation which is shown below
[tex]= (\frac{4m^4n^{16}}{9}) ^\frac{1}{2}[/tex]
So,
[tex]= (\frac{(2)^2(m^2)^2(n^8)^2}{(3)^2} ^\frac{1}{2}[/tex]
Which gives result
[tex]= \frac{2m^2n^8}{3}[/tex]