This was the explanation to the answer on a college algebra CLEP test: Since $(64a^6)^{1/6} = (64^{1/6})\times(a^6)^{1/6} = 2 \times|a| = 2|a|$
Why is $a$ an absolute value? $a^6$ will equal a positive number regardless if $a$ is positive or negative, so I don't see the purpose of taking the absolute value of $a$.
You said it yourself: "$a^6$ will equal a positive number regardless if $a$ is positive or negative".
So then you can always take the sixth root, regardless of whether $a$ was positive or negative. That sixth root is a positive number of the same magnitude as $a$.
So how do you write that in a formula?