# decimal exponents

#### anthonye

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.

#### Shakarri

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.

#### anthonye

Ok thanks How do you handle an irrational exponent?

#### Shakarri

There is not really a useful way to manipulate $$\displaystyle 2^{\pi}$$ but any scientific calculator will handle decimal and irrational powers just fine

• 1 person

#### anthonye

Ok Thanks for that.

#### DenisB

3^(4e) = (3^4)^e or (3^e)^4

#### HallsofIvy

MHF Helper
Every real number can be written as a limit of a sequence of rational numbers. For example, $\pi$ 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.