How to calculate limit as x approaches infinity of a^x/b^x? I'm trying to calcululate $\lim_{x\to\infty}\frac{a^x}{b^x}$.
I've done a few examples on Wolfram Alpha, and it seems if $a>b$ it goes to infinity and if $a<b$ it goes to $0$, but I am not sure how to prove it.
L'Hopital is normally what I would try, but it doesn't seem to work here because it doesn't really change the structure of the numerator or denominator.

Hint: review properties of exponents, especially that the quotient of two numbers each raised to the the $x$ power is equal to the quotient of the two numbers itself raised to the $x$ power. 
