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