Answer:
m=2 and n=3
Step-by-step explanation:
Step :-
Given [tex][ 2 x^{n}y^{2} ]^m = 4 x^6 y^4[/tex]
using algebraic formula [tex](a^m)^n= a^{mn}[/tex]
now
[tex]2^{m} x^{mn} y^{2m} = 4x^{6} y^{4}[/tex]
now equating 'x' powers, we get
[tex]x^{mn} = x^{6}[/tex]
[tex]mn=6[/tex] ....(1)
now
[tex]y^{2m} = y^{4}[/tex]
Equating 'y' powers ,we get
2 m=4
m=2
substitute m= 2 in equation (1)
we get
2 n=6
n=3
verification:-
substitute m=2 and n=3 , we get
[tex][ 2 x^{n}y^{2} ]^m = 4 x^6 y^4[/tex]
[tex](2 x^{3} y^2)^2 = 4 x^6 y ^4\\[/tex]
[tex]4 x^6 y^4 = 4 x^6 y^4[/tex]
both are equating so m= 2 and n=3
