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7-\sqrt[3]{\frac{3\times 8+3}{8}}
Calculate \sqrt[3]{343} and get 7.
7-\sqrt[3]{\frac{24+3}{8}}
Multiply 3 and 8 to get 24.
7-\sqrt[3]{\frac{27}{8}}
Add 24 and 3 to get 27.
7-\frac{3}{2}
Calculate \sqrt[3]{\frac{27}{8}} and get \frac{3}{2}.
\frac{11}{2}
Subtract \frac{3}{2} from 7 to get \frac{11}{2}.