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

Sep 25, 2015

It's ${5}^{24}$
Dealing with powers of powers is really simple: you only need to multiply the exponents. Namely, ${\left({a}^{b}\right)}^{c} = {a}^{b c}$.
This is a consequence of the fact that ${a}^{b} \cdot {a}^{c} = {a}^{b + c}$: take your case as an example.
By definition, ${\left({5}^{8}\right)}^{3}$ means ${5}^{8} \cdot {5}^{8} \cdot {5}^{8}$. According to the rule above, this expression simplifies into ${5}^{8 + 8 + 8}$, which is indeed ${5}^{8 \cdot 3}$