81^-0,75+1/125^-1/3-1/32^-3/5

To simplify the expression given, we can first rewrite each term in terms of positive exponents: \(81^{-0.75} = \frac{1}{81^{0.75}} = \frac{1}{(3^4)^{0.75}} = \frac{1}{3^{3}} = \frac{1}{27} \) \( \frac{1}{125^{-1/3}} = 125^{1/3} = \sqrt[3]{125} = 5\) \( \frac{1}{32^{-3/5}} = 32^{3/5} = \sqrt[5]{32^3} = \sqrt[5]{32^3} = \sqrt[5]{32768} = 8\) Now we can substitute these values back into the expression: \( \frac{1}{27} + 5 - 8 = \frac{1}{27} - 3 \) At this point, to add fractions with unlike denominators, we need to find a common denominator. The common denominator for \(27\) and \(1\) is \(27\), so the expression becomes: \( \frac{1}{27} - \frac{81}{27} = \frac{1 - 81}{27} = \frac{-80}{27}\) Therefore, the simplified form of the expression is \( \frac{-80}{27} \).