Answer:
[tex]3m^{10}n^{-11}[/tex]
Step-by-step explanation:
Given the expression [tex]\frac{(3m^{-1}n^{2})^{-4} }{(2m^{-2}n)^{3} }[/tex], we will use laws of indices to get the equivalent expression as shown below;
According to one of the law of indices,
[tex]\frac{a^{m} }{a^{n} } = a^{m-n} \ and\ (a^{m})^{n} = a^{mn}[/tex]
[tex]\frac{(3m^{-1}n^{2})^{-4} }{(2m^{-2}n)^{3} }\\= \frac{3m^{4}n^{-8} }{2m^{-6}n^{3} }\\= 3m^{(4-(-6))} * n^{-8-3}\\ = 3m^{10}n^{-11}[/tex]
This gives the required expression
