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Question
Show that:\[\sqrt[3]{- 125 - 1000} = \sqrt[3]{- 125} \times \sqrt[3]{- 1000}\]
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Solution
LHS = \[\sqrt[3]{- 125 \times - 1000} = \sqrt[3]{- 5 \times - 5 \times - 5 \times - 10 \times - 10 \times - 10} = \sqrt[3]{\left\{ - 5 \times - 5 \times - 5 \right\} \times \left\{ - 10 \times - 10 \times - 10 \right\}} = - 5 \times - 10 = 50\]
RHS = \[\sqrt[3]{- 125} \times \sqrt[3]{- 1000} = \sqrt[3]{- 5 \times - 5 \times - 5} \times \sqrt[3]{\left\{ - 10 \times - 10 \times - 10 \right\}} = - 5 \times - 10 = 50\]
Because LHS is equal to RHS, the equation is true.
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