What is this equation formally?

Question

Having fun with the calculator, I realized that :

(a^c) and (a^b)

with c > b and c > 4 and b = 2

a^c / a^b = a^(c-2)

So, for example:

3^5 / 3^2 = 27 is same that 3^(5-2) => 27

I know it's basic, but how is this happening?

What is this formally called? I realized thinking "How often is this greater than this other"

I think it's "exponential growth"

Answer 1

Congrats, you discovered the rule of division with powers:

$$ \frac{b^m}{b^n} = b^{m-n} $$

Answer 2

A fraction with five factors equal to $3$ in the numerator, and two factors $3$ can be simplified by the elementary rules on fractions.