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\sqrt[3]{-1000}+\sqrt[5]{\left(-7\right)^{5}}
Calculate -10 to the power of 3 and get -1000.
-10+\sqrt[5]{\left(-7\right)^{5}}
Calculate \sqrt[3]{-1000} and get -10.
-10+\sqrt[5]{-16807}
Calculate -7 to the power of 5 and get -16807.
-10-7
Calculate \sqrt[5]{-16807} and get -7.
-17
Subtract 7 from -10 to get -17.