# Can you raise a number to the power of another number being raised to a power?

So I actually have two questions.

1. Is it even Possible to raise a number to the power of a number with its own exponent? Kind of like an exponent within an exponent....? It doesn't sound right to me but here is why I ask (also my second question)

2. The equation is: $y=3E-15e^{0.0197x}$

I know the E stands for exponential notation so that would be $3*10^{-15}$, then is that multiplied by $e^{0.0197x}$ or is the $e^{0.0197x}$ part of the power of the exponential notation? (I really hope that makes sense...)

So the reason for my first question is because if the equation was $3*10^{(-15e^{0.0197x})}$ Then you would have to raise $10$ to the power of $-15e$ which is also being raised to a power... It sounds like a pyramid scheme to me 😜

****I'm far from stupid but I have absolutely no problem with your answers being "dumbed" down.

• You know about using nested levels of parentheses, right? Same thing. I presume you aren't baffled by $1+(1+(1+1))$... – MPW Apr 23 '16 at 4:53
• In math we don't use scientific number notation like 3E-15, instead we write what it means: $3\times10^{-15}$. – Marc van Leeuwen Apr 23 '16 at 4:59
• Marc van Leeuwen I have seen quite a few of your answers amongst different posts and you are quite sassy! I'm not baffled by anything hear just asking a question because it's a homework assignment and I like to get good grades instead of assuming I know everything and making mistakes! And in math we do use Exponential Notation otherwise I wouldn't be dealing with it in my College Algebra coarse! – user7075 Apr 23 '16 at 5:43

## 1 Answer

Any power of a positive number is just another number. You can do anything with that number that you can do with numbers, including using them as exponent to another positive number.

However $y=$3E-15$e^{0.0197x}$ would stand for $y=3\times 10^{-15}\times e^{0.0197x}$, since the E notation only accepts an explicit integer, and the power of $e$ just has to be multiplied with the number that preceeds it. So in this case there is no repeated exponentiation.