Answer:
[tex]\frac{81m^2n^5}{8}[/tex]
Step-by-step explanation:
We are given the following expression and we are to simplify it:
[tex] \frac { (3 m^ {-1} n^2 )^ 4} {( 2m ^ {-2} n ) ^3} [/tex]
Expanding the terms in both the numerator and the denominator by multiplying them with their whole powers to get:
[tex] = \frac{3^4m^{-4}n^8}{2^3m^{-6}n^3}[/tex]
[tex]=\frac{81m^{(-4+6)}n^{(8-3)}}{8}[/tex]
Cancelling all the like terms to get:
[tex]=\frac{81m^2n^5}{8}[/tex]
Therefore, option B is the correct answer.
