Answer
$\dfrac{a^m}{a^n}=a^{m-n}$
Work Step by Step
Since, $\dfrac{a^m}{a^n}=a^m \times \dfrac{1}{a^n}$
Also, $a^{-n}=\dfrac{1}{a^n}$
Thus, $a^m \dfrac{1}{a^n}=a^m a^{-n}$ ...(1)
Now, we need to use the product of powers property.
$a^{m}a^{-n}=a^{m-n}$
Equation (1) becomes: $a^m \dfrac{1}{a^n}=a^m a^{-n}=a^{m-n}$
This gives: $\dfrac{a^m}{a^n}=a^{m-n}$
Hence, the result has been verified.
