You use the reciprocal of (3/5) because a number to a negative exponent is the same as 1 over the number to the positive form of the exponent.
So - (3/5) ^ -2 is the same as - (1/(3/5)) ^ 2.
So:
$${\mathtt{\,-\,}}\left({\left({\frac{{\mathtt{3}}}{{\mathtt{5}}}}\right)}^{-{\mathtt{2}}}\right) = {\mathtt{\,-\,}}{\frac{{\mathtt{25}}}{{\mathtt{9}}}} = -{\mathtt{2.777\: \!777\: \!777\: \!777\: \!777\: \!8}}$$
And $${\mathtt{\,-\,}}\left({\left({\frac{{\mathtt{5}}}{{\mathtt{3}}}}\right)}^{{\mathtt{2}}}\right) = {\mathtt{\,-\,}}{\frac{{\mathtt{25}}}{{\mathtt{9}}}} = -{\mathtt{2.777\: \!777\: \!777\: \!777\: \!777\: \!8}}$$
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