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"

A beautiful isomorphism between $\langle \Bbb R,+ \rangle$ and $\langle \Bbb R_{>0}, \cdot \rangle$. — Kenny Lau, Sep 11 '17 at 19:09
Assuming $c>b$,$$\frac{a^c}{a^b}=\frac{\overbrace{a\times\dots\times a}^c}{\underbrace{a\times\dots\times a}_b}=\overbrace{a\times\dots\times a}^{c-b}=a^{c-b}$$ — Simply Beautiful Art, Sep 11 '17 at 19:37

score 3 · Accepted Answer · answered Sep 11 '17 at 19:09

3

Congrats, you discovered the rule of division with powers:

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

answered Sep 11 '17 at 19:09

Sean Roberson

Oh, I suppose that's how intellectuals thought in antiquity – ESCM Sep 11 '17 at 19:26

score 0 · Answer 2 · answered Sep 11 '17 at 19:14

0

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

answered Sep 11 '17 at 19:14

Bernard

2 Answers2