decimal exponents

Jul 2010
614
5
HI;
Just need to know how to tackle expressions like this 3^1.2

what I did was 3^(12/10) = 3^(6/5) = 5root3^6.

Thanks.
 
Oct 2012
751
212
Ireland
The approach you took was correct but it wont always work. If you have an irrational number in the power such as \(\displaystyle 2^{\pi}\) then you cannot break it into nice looking numbers like you did.
 
Jul 2010
614
5
Ok thanks How do you handle an irrational exponent?
 
Oct 2012
751
212
Ireland
There is not really a useful way to manipulate \(\displaystyle 2^{\pi}\) but any scientific calculator will handle decimal and irrational powers just fine
 
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Feb 2015
2,255
510
Ottawa Ontario
3^(4e) = (3^4)^e or (3^e)^4
 

HallsofIvy

MHF Helper
Apr 2005
20,249
7,909
Every real number can be written as a limit of a sequence of rational numbers. For example, [itex]\pi[/itex] is the limit of the sequence 3, 3.1, 3.14, 3.1415, 3.14159, 3.141592, 3.1415926, etc. So the definition of, say, \(\displaystyle 2^{\pi}\) is the limit of the sequence \(\displaystyle 2^3\), \(\displaystyle 2^{3.1}\), \(\displaystyle 2^{3.14\), \(\displaystyle 2^{3.1415}\), etc. And each of those, of course, is 2 to a rational number power.