3的m次幂等于6,27的n次幂等于2,求3的2m+4n的次幂等于多少?

题目

3的m次幂等于6,27的n次幂等于2,求3的2m+4n的次幂等于多少?
如上

答案

3^m=6
27^n=(3^3)^n=2
3^3n=2
(3^n)^3=2
3^n=2^(1/3)
3^(2m+4n)
=3^2m*3^4n
=(3^m)^2*(3^n)^4
=6^2*[2^(1/3)]^4
=36*2^(4/3)
=72*2^(1/3)