Question

How do you simplify `(5^8)^3`?

Answer 1

It's `5^24`

Explanation:

Dealing with powers of powers is really simple: you only need to multiply the exponents. Namely, `(a^b)^c=a^{bc}`.

This is a consequence of the fact that `a^b * a^c = a^{b+c}`: take your case as an example.

By definition, `(5^8)^3` means `5^8 * 5^8 * 5^8`. According to the rule above, this expression simplifies into `5^{8+8+8}`, which is indeed `5^{8*3}`