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**Prove It** The same rules apply as when they are square roots. The only difference is now you have to find a CUBIC factor, rather than a square factor...

Note that $\displaystyle 16 = 8\cdot 2$

So $\displaystyle \sqrt[3]{16} = \sqrt[3]{8\cdot 2} = \sqrt[3]{8}\cdot\sqrt[3]{2} = 2\cdot\sqrt[3]{2}$.

Also, note that $\displaystyle 54 = 27\cdot 2$.

So $\displaystyle \sqrt[3]{54} = \sqrt[3]{27\cdot 2} = \sqrt[3]{27}\cdot\sqrt[3]{2} = 3\cdot\sqrt[3]{2}$.

Therefore $\displaystyle \sqrt[3]{16} + 3\cdot\sqrt[3]{54} = 2\cdot\sqrt[3]{2} + 9\cdot\sqrt[3]{2} = 11\cdot\sqrt[3]{2}$.