If `m=a^x` and `n=a^y` , then `m^y.n^x`

If 1/ (m+i n) - (x-iy)/(x+iy) =0, where x,y,m,n are real and x+iy!=0 and m+i n!=0 , prove that m^2+n^2=1 .

If x=a^(m+n),y=a^(n+1) and z=a^(l+m) prove that x^(m)+y^(n)z^(l)=x^(n)y^(l)z^(m)

If x=a^(m+n),y=a^(n+1) and z=a^(l+m) prove that x^(m)+y^(n)z^(l)=x^(n)y^(l)z^(m)

If x=a^(m+n),y=a^(n+l) and z=a^(l+m), prove that x^(m)y^(n)z^(l)=x^(n)y^(l)z^(m)

If y^(m)x^(n)=(x+y)^(m+n) , then find dy/dx

If x and y are positive real numbers and m,n are any positive integers,then (x^(n)y^(m))/((1+x^(2n))(1+y^(2m)))<(1)/(4)

If m and n are theorder the degree of the differential equation (y_(2))^(5)+(4(y_(2))^(3))/(y_(3))+y_(3)=x^(2)-1, then m=3,n=3 b.m=3,n=2cm=3,n=5d*m=3,n=1

If l + m + n = 0, then the system of equations -2x + y + z = l x - 2y + z = m x + y - 2z = n has