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

1 Answer
Sep 25, 2015

Answer:

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}#