If (a ^ m + 1 × B ^ n + 2) × (a ^ 2N-1 × B ^ 2m) = a ^ 5B ^ 6, find the value of M + n

If (a ^ m + 1 × B ^ n + 2) × (a ^ 2N-1 × B ^ 2m) = a ^ 5B ^ 6, find the value of M + n


(a^m+1×b^n+2)×(a^2n-1×b^2m)=a^5b^6
a^(m+1+2n-1)×b^(n+2+2m)=a^5b^6
therefore
m+2n=5
2m+n+2=6
So m = 1, n = 2



Given a ^ m = 6, a ^ n = 9, find the value of a ^ M-N, a ^ 2m + n


a^m-n=a^m/a^n=6/9=2/3
a^2m+n=a^2m*a^n=(a^m)^2*a^n=6^2*9=36*9=324



Given that M is the sum of the opposite number of - 5 and - 12, and that n is 5 greater than - 6, find m and n


Because the opposite of - 5 is 5, M = 5 + (- 12) = - 7
n=-6+5=-1