Question

如果2^（2m+n)×2^5=2^10,3^4m-2n=3^9,则m^m × m^n= 2^(2m+n)那个^，就是方。2^(2m+n)是2的2m+n次方

如果2的(2m+n)次方*2的5次方,3的(4m-2n)*3的3次方=3的9次方,
2^(2m+n+5)=2^10,(4m-2n+3)=3^9
(2m+n+5)=10 4m-2n+3=9
2m+n+5-(4m-2n+3)=10-9
2m+n+5-4m+2n-3=1
-2m+3n+5=1
-2m+3n=-4
2m+n+5+(4m-2n+3)=10+9
6m-n+8=19
6m-n=11
6m-n+(-2m+3n)=-4+11
6m+(-2m)+2n=7
4m+2n=7
2(2m+n)=4m+2n=7 2m+n=3.5=
m^m × n^n=m^m+n....................................................

Answer 1

2^(2m+n)×2^5 = 2^10
2^(2m+n+5) = 2^10
2m + n + 5 = 10
2m + n = 5

3^(4m-2n) = 3^9
4m - 2n = 9
2m - n = 4.5

解得：
m = 2.375
n = 0.25

所以：
m^m × m^n = m^(m+n) = 2.375^2.625 = 9.685
2^(2m+n) = 2^5 = 32