Right limit to zero

Question

I have to solve this right limit

$$\lim_{a\to 0+} ab \text{ with }b=\frac{a^2e^{a^{3}}}{e^{a^{3}}-1} $$

But thinking since $a$ goes to zero, it becomes $0b$ = $0$. This answer would of course be too simple so maybe I'm mistaken with what a right limit exactly is. I thought a left or right limit only exists in a system with two equations, eg:

$$-x^2+3 \text{ when } x \leqslant 1$$ $$\frac{1}{2}x+1 \text{ when } x>1 $$

Answer 1

HINT
Letting $x=a^3$ the expression becomes $$\dfrac{e^x}{(e^x-1)/x}$$