Simplify Exponential Output

[davef]

4^(0.5x) can be rewritten as 2^x (i.e., 2^[(2)(0.5)(x)]).

How can I get Mathematica to output 4^0.5x as 2^x?

E.g., my input is 4^(.5 x); how do I get output of 2^x?

[Nasser M. Abbasi]

"davef" <davidfr...@yahoo.com> wrote in message
news:hng268$s1j$1...@smc.vnet.net...

> 4^(0.5x) can be rewritten as 2^x (i.e., 2^[(2)(0.5)(x)]).
>
> How can I get Mathematica to output 4^0.5x as 2^x?
>
> E.g., my input is 4^(.5 x); how do I get output of 2^x?
>

If you Rationalize[] the value you are multiplying x with first, then you
can use simplify,

In[10]:= a = 0.5;

Simplify[4^(Rationalize[a]*x)]

Out[11]= 2^x

--Nasser