Simplify each of the following:(i) \(\sqrt[3]{4}\) x \(\sqrt[3]{16}

1.	Simplify each of the following:(i) \(\sqrt[3]{4}\) x \(\sqrt[3]{16}\)(ii) \(\frac{\sqrt[4]{1250}}{\sqrt[4]{2}}\)
Answer» (i) \(\sqrt[3]{4}\) x \(\sqrt[3]{16}\) = \(\sqrt[3]{4\times 16}\) = \(\sqrt[3]{64}\) = \(\sqrt[3]{4^3}\) = \((4^3)^\frac{1}{3}\) = 4 (ii) \(\frac{\sqrt[4]{1250}}{\sqrt[4]{2}}\) = \(\sqrt[4]\frac{1250}{2}\) = \(\sqrt[4]\frac{625\times 2}{2}\) = \(\sqrt[4]{625}\) = \(\sqrt[4]{5^4}\) = (5⁴)^{\(\frac{1}{4}\)} = 5

Simplify each of the following:(i) \(\sqrt[3]{4}\) x \(\sqrt[3]{16}\)(ii) \(\frac{\sqrt[4]{1250}}{\sqrt[4]{2}}\)

Answer»

(i) \(\sqrt[3]{4}\) x \(\sqrt[3]{16}\)

= \(\sqrt[3]{4\times 16}\) = \(\sqrt[3]{64}\)

= \(\sqrt[3]{4^3}\) = \((4^3)^\frac{1}{3}\) = 4

(ii) \(\frac{\sqrt[4]{1250}}{\sqrt[4]{2}}\) = \(\sqrt[4]\frac{1250}{2}\)

= \(\sqrt[4]\frac{625\times 2}{2}\) = \(\sqrt[4]{625}\)

= \(\sqrt[4]{5^4}\) = (5⁴)^{\(\frac{1}{4}\)} = 5

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