Finding the flaw in $-12=(-12)^1=(-12)^{6/6}=\cdots=12$

Question

I was tutoring today and came across a question that I was incapable of explaining sufficiently. It stems from the following false string of equalities...

$$-12=(-12)^1=(-12)^\frac{6}{6} =((-12)^6)^\frac{1}{6} =((-1)^6 12^6)^\frac{1}{6}=(12^6)^\frac{1}{6}=12$$

If anyone can explain the false step (Im assuming the third “=“), why this string of equalities is wrong, and how to avoid making it that would be most helpful for when I need to explain it again.

Answer 1

$-12=(-12)^1=(-12)^\frac{6}{6} =((-12)^6)^\frac{1}{6}$

Last step above is wrong, because of the arbitrary convention that a positive number (i.e. $[(-12)^6]$) when taken to the $(1/6)$ power is equal to a positive number, not a negative number.