Question

How do I visualise the power of a number?

Something that often helps me when thinking abstractly, is visualizing scalars as one-dimensional vectors.

For example,
I can visualize
+ as translation,
- as inverse translation,
* as scale,
/ as inverse scale,
abs() as distance from zero,

But I am not sure how to visualize a power.
I know what it does eg:
a^b = "a times itself, b times"

But I can't seem to visualize it.
Can someone help me?