The expression which is equivalent to the given expression is [tex]\frac{27 m^{5}}{n}[/tex]
Evaluating indices
From the question, we are to determine the expression which is equivalent to the given expression
The given expression is
[tex]\frac{(3m^{2}n)^{3} }{mn^{4} }[/tex]
Clearing the brackets, we get
[tex]\frac{3^{3} m^{2(3)}n^{3} }{mn^{4} }[/tex]
Simplifying, we get
[tex]\frac{27 m^{6}n^{3} }{mn^{4} }[/tex]
Then,
[tex]27 m^{6-1}n^{3-4}[/tex]
[tex]27 m^{5}n^{-1}[/tex]
= [tex]\frac{27 m^{5}}{n}[/tex]
Hence, the expression which is equivalent to the given expression is [tex]\frac{27 m^{5}}{n}[/tex]
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