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-3-\left(\frac{25}{9}\right)^{-1}
Calculate \sqrt[3]{-27} and get -3.
-3-\frac{9}{25}
Calculate \frac{25}{9} to the power of -1 and get \frac{9}{25}.
-\frac{84}{25}
Subtract \frac{9}{25} from -3 to get -\frac{84}{25}.