若2的m次方=3,4的n次方=5.则2的m+2n次方=?

2^m = 3 ①
4^n = 5 ②
则 2^(m + 2n)
2^(m + 2n) = 2^m * 2^(2n) -----用到 A^(B + C) = (A^B) * (A^C)
= 2^m * 4^n -----用到 A^(BC) = (A^B) ^ C 即：2^(2n) = (2^2) ^ n = 4^n
= 3 * 5
= 15
补充：根据 4^n = 2^(2n) = 5 和 2^m = 3 进一步可得到：2^(2n - m) = 5 / 3 = 1.666666