若256x=25•211,则x=________;若am=3,an=5,则am-n=________,a3m-2n=________.
2
![](http://thumb.1010pic.com/pic5/latex/21000.png)
分析:根据乘方的意义把256
x化为以2为底数的幂,再根据同底数幂相乘,底数不变指数相加进行计算,然后根据指数相等解答;
逆运用同底数幂相除,底数不变指数相减解答即可.
解答:∵256
x=(2
8)
x=2
8x,2
5•2
11=2
5+11=2
16,
∴8x=16,
解得x=2;
∵a
m=3,a
n=5,
∴a
m-n=a
m÷a
n=
![](http://thumb.1010pic.com/pic5/latex/14.png)
,
a
3m-2n=a
3m÷a
2n=(a
m)
3÷(a
n)
2=3
3÷5
2=
![](http://thumb.1010pic.com/pic5/latex/21000.png)
.
故答案为:2;
![](http://thumb.1010pic.com/pic5/latex/14.png)
;
![](http://thumb.1010pic.com/pic5/latex/21000.png)
.
点评:本题主要考查了同底数幂相除,底数不变指数相减的性质,有理数乘方的意义,熟记性质并灵活运用是解题的关键.