Simplify each of the following:
$ \sqrt[3]{4} \times \sqrt[3]{16} $

Given:

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

To do: 

We have to simplify the given expression.

Solution:

We know that,

$(a^{m})^{n}=a^{m n}$

$a^{m} \times a^{n}=a^{m+n}$

$a^{m} \div a^{n}=a^{m-n}$

$\sqrt[n]{a} \times \sqrt[n]{b}=\sqrt[n]{a \times b}$

$a^{0}=1$

Therefore,

$\sqrt[3]{4} \times \sqrt[3]{16}=\sqrt[3]{4 \times 16}$

$=\sqrt[3]{64}$

$=\sqrt[3]{4 \times 4 \times 4}$

$=\sqrt[3]{4^3}$

$=4$

Hence, $\sqrt[3]{4} \times \sqrt[3]{16}=4$.

Tutorialspoint

Updated on: 10-Oct-2022

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