Answer:
[tex]-\frac{4m^{4}n^{2}}{9}[/tex]
Step-by-step explanation:
The given expression is
[tex]=\frac{(2m^3n^2)^3}{-18m^5n^4}[/tex]
Use the power rule of indices on the denominator;[tex](a^m)^n=a^{mn}[/tex]
[tex]=\frac{8m^9n^6}{-18m^5n^4}[/tex]
We apply the quotient rule of indices; [tex]\frac{a^m}{a^n} =a^{m-n}[/tex]
[tex]=\frac{8m^9n^6}{-18m^5n^4}[/tex]
[tex]=-\frac{4m^{9-5}n^{6-4}}{9}[/tex]
Simplify
[tex]=-\frac{4m^{4}n^{2}}{9}[/tex]
