Question

What expression is equivalent to a^m divided by a^n?

Answer 1

$a^m=\underbrace{a\cdot a\cdot a\cdot...\cdot a}_m\\\\a^n=\underbrace{a\cdot a\cdot a\cdot...\cdot a}_n\\\\a^m:a^n=\dfrac{a^m}{a^n}=\dfrac{\overbrace{a\cdot a\cdot a\cdot...\cdot a}^m}{\underbrace{a\cdot a\cdot a\cdot...\cdot a}_n}=a^{m-n}\\\\\boxed{a^m:a^n=a^{m-n}}$