Simplify and express the result in its simplest form: $\sqrt[3]{32} \times \sqrt[3]{250}$ .

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Solution

Consider $\sqrt[3]{32} \times \sqrt[3]{250}$ and solve as follows:

$\sqrt[3]{32} \times \sqrt[3]{250} = \sqrt[3]{2 \times 2 \times 2 \times 2 \times 2} \times \sqrt[3]{2 \times 5 \times 5 \times 5} = (\sqrt[3]{4} \times \sqrt[3]{{(2)}^{3}}) \times (\sqrt[3]{2} \times \sqrt[3]{{(5)}^{3}})$
$= (\sqrt[3]{4} \times 2) \times (\sqrt[3]{2} \times 5) = (\sqrt[3]{4} \times \sqrt[3]{2}) \times (2 \times 5) = \sqrt[3]{8} \times 10 = \sqrt[3]{{(2)}^{3}} \times 10 = 2 \times 10 = 20$ .

Hence, $\sqrt[3]{32} \times \sqrt[3]{250} = 20$ .

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