What is wrong with this proof?
$-3 = \sqrt[3]{-27} = {(-27)}^{\frac 13} = {(-27)}^{\frac 26} = \sqrt[6]{{(-27)}^2} = \sqrt[6]{{27}^2} = {(27)}^{\frac 26} = {(27)}^{\frac 13} = \sqrt[3]{27} = 3$
This is obviously false since $-3 \neq 3$.
But still I can't figure out which equation is the wrong one and why that is.
Thanks in advance for anyone who will help.