Question 7150
Well, your first step is ok:


{{{(243)^(-2/5)}}} = {{{1/(243)^(2/5)}}}

Finding the square of a number is relatively easy.
Finding the fifth root of a number isn't. But you can do both with your calculator.

Type in 243 then ^ then (2/5) then hit the enter or = key.

You should get: {{{(243)^(2/5) = 9}}}

So the answer of 1/9 is correct.