What is $x^y$? How to understand it?

I have one pen. I become really angry and I break it into $x$ pieces. Each time I get angry I break each of my pieces into $x$ even tinier pieces. I become angry $y$ times. I end up with $x^y$ pieces.


$2\cdot 4$: $$\underbrace{2+2+2+2}_{4\text{ twos}}$$

$2^4$: $$\underbrace{2\cdot 2\cdot 2\cdot2}_{4\text{ twos}}$$