I'm trying to figure how how 13^3 = 2197 but can't produce the same value and this is how I'm doing it:

13+13+13 =39  
39+39+39 = 115

and etc....  And this is because I figured if 2^1 = 2 and 2^2 =4 then you take the product of the remaining number and times it to the power of two but with 13^3 I take 13 and times it to the power of 3 then take the remaining product and times it to the power of 3 as well...

Is it my method or am I adding it wrong ? Can someone help me out here ? cause I'm trying to grasp the way decimals (which to the power of ten I think) and hexadecimal and Binary works due to my desire of furthering my understanding of how ASM language works and how logical gates can cause a computers processor to add, subtract, multiply and divide with positive and negative numbers....

Like I said before, this kind of stuff fascinates me and I want to quench my curiosity of everything to do with how machines operates and what makes computers tick...

Isn't 39+39+39 117?

I'm not sure I understand how you're getting 13+13+13 or 39+39+39.

13^3 is 13 multiplied by itself three times, i.e., 13×13×13 = 169×13 = 2197.

Oh so you times it instead ? I guess this caused by my ignorance of basic math... There's no hope for me if I can't even do basic addition .... :/

It's one multiplied by thirteen three times.  This is why x⁰ (for all x, such that x is a non-zero number) is always equal to one.  1*13*13*13=13³ or 1*13*13=13² or 1*13=13¹ 1=13⁰

(In your middle school math class, they'll tell you it's "just because it is" but my explanation is more logical and consistent)

That's nice that your school was generous enough to let you take a normal math class but I guess some of us weren't so fortunate enough to have that privilege..  

I wouldn't know a d*** thing about middle school math since I was bounced around from school to school and only experienced math in special ED.... And none of the new schools were able to keep the same curriculum I was taking for math nor be able to successfully transfer my transcript papers from my previous schools.

So yeah, I was being bounced around on the math class which is why I'm having trouble with most of the basic math and don't know a d*** thing about algebra.... :/

Well, it's alright.  The information is not proprietary, so you'll pick it up.

It's called a power, 13^3 is "13 to the power of 3".
Power of 1 is just an identity function, so
n^1 = n
n^2 = n*n
n^3 = n*n*n
And so on