$\displaystyle \left( \frac{a^{-3/m} \cdot b^{6/n}}{a^{-6/m} \cdot b^{9/n}}\right)^{-1/3} $

thats the orginal problem, heres my work

$\displaystyle \left( \frac{a^{6/m} \cdot b^{6/n}}{a^{3/m} \cdot b^{9/n}}\right)^{-1/3} $

$\displaystyle \left( {a^{3/m} \cdot b^{-3/n}}\right)^{-1/3} $

ok iam having extreme difficulty w/ latex past this point so ill write out what i did from this step, so i flipped them again w/ the positive b^3/n on top and a^3/m on bottom, then applied the positive 1/3 to each and my wrong answer is b^n over a^m

the answer from a algebra problem solver i have is 1/a^1/m b^5/n

i have no idea where i went wrong, sorry i couldnt finish up in latex