How to solve for a number if its exponent is less than 1 but greater than 0 like 1/2 First off, I know how to solve for negative exponents. The inquiry is how to solve for the number if the exponent is like 0.5 or 1/2. I found this forum post which talked about the reasons it is possible and that it works.
How does an exponent work when it's less than one?
It is nice to understand that it works however I am having a hard time trying to figure out the exact math you need to do; to solve for like, $\\36^.5$
I know I can just use a calculator however I am trying to actually make a calculator and I need to know how to do this to incorporate this into it.
Thanks in advance.
 A: If the exponent that you want to solve for is a rational number (meaning it can be written as a fraction) it is solvable/approximate-able. 
To do this, you need to understand the properties of exponential functions. One such property says that $a^{bc} = (a^b)^c$. When the exponent is rational and can be written as a fraction, for example, $\frac23$, it can be rewritten as $2\frac13$ and split into 2 math operations.
First, you take the number a that you want to put to the power of$ \frac23$ and put it to the power of the first number b or in this case $2$ and do $a^2$, and then take that number and raise it to the power of $\frac13$.
As it says in the original forum, taking something to a fraction power $\frac1c$ is the same as taking the $c^{th}$ root of that number so the final product of raising $a^{(\frac23)}$ is the same as the $3^{rd}$ root of $a^2$.
And you cant really take the root of a number exactly because most of the time it will be irrational (not expressed as a fraction), but you can approximate it using calculus, or to figure out what numbers it is between numerically. 
