exponent rule when dividing the same exponents

Question

I ran into a bit of confusion when applying the exponent rule: $x^a/x^b = x^{a-b}$

Then when $4^x/2^x$ why does it equal $2^x$ if we apply the rule above then wouldn't it be: $(4/2)^{x-x}$ ?

Thank you!

Answer 1

As $4$ and $2$ are different, this rule does not apply !

What you can use is

$$\frac{a^x}{b^x}=\left(\frac ab\right)^x.$$

Answer 2

HINT:

$4=2^2$ so $4^x=(2^2)^x=2^{2x}$