Question

已知3的M次方=4,3的N次方=5，求3的（2M+3N+1）次方的值

Answer 1

3^（2M+3N+1）
=(3^m)^2*(3^n)^3*3
=16*125*3
=6000

追问

已知3^m*9^m*27^m*81^m=3^40,求M的值

追答

3^m*9^m*27^m*81^m=3^40
3^m*3^2m*3^3m*3^4m=3^40
3^(m+2m+3m+4m)=3^40
3^10m=3^40
10m=40
m=4

追问

9^m*9=3^10
m=?

追答

9^m*9=3^10
9^(m+1)=3^10=(3^2)^5=9^5
m+1=5
m=4

Answer 2

3^(2m+3n+1)
=3*(3^m)^2*(3^n)^3
=3*4^2*5^3
=3*16*125
=3*2*8*125
=6*1000
=6000

追问

对不起,我是初一的,能解得详细些吗

追答

3^(2m+3n+1)
=3^2m*3^3n*3
=3*3^2m*3^3n
=3*(3^2)^m*(3^n)^3