Question

itle=" \sqrt[3]{64a {}^{3} b {}^{3} } " alt=" \sqrt[3]{64a {}^{3} b {}^{3} } " align="absmiddle" class="latex-formula">
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Answer 1

Answer:

$\boxed{4ab}$

Step-by-step explanation:

$= > \sqrt[3]{64 {a}^{3} {b}^{3} } \\ \\ = > \sqrt[3]{(4 \times 4 \times 4 ) {a}^{3} {b}^{3} } \\ \\ = > \sqrt[3]{ {4}^{3} {a}^{3} {b}^{3} } \\ \\ = > \sqrt[3]{ {(4ab)}^{3} } \\ \\ = > {(4ab)}^{ \cancel{3} \times \frac{1}{ \cancel{3}} } \\ \\ = > 4ab$

Answer 2

Answer:

$=4ab$

Step-by-step explanation:

$\sqrt[3]{64a^3b^3}\\\mathrm{Apply\:radical\:rule\:}\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b},\:\quad \mathrm{\:assuming\:}a\ge 0,\:b\ge 0\\=\sqrt[3]{64}\sqrt[3]{a^3}\sqrt[3]{b^3}\\\sqrt[3]{64}=4\\=4\sqrt[3]{a^3}\sqrt[3]{b^3}\\\mathrm{Apply\:radical\:rule\:}\sqrt[n]{a^n}=a,\:\quad \mathrm{\:assuming\:}a\ge 0\\\sqrt[3]{a^3}=a\\=4a\sqrt[3]{b^3}\\\mathrm{Apply\:radical\:rule\:}\sqrt[n]{a^n}=a,\:\quad \mathrm{\:assuming\:}a\ge 0\\\sqrt[3]{b^3}=b\\=4ab$