\sqrt[3]{64a {}^(3) b {}^(3) } ​

Question

`\sqrt[3]{64a {}^(3) b {}^(3) }`
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Answer 1

`\boxed{4ab}`

Explanation:

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

Answer 2

`=4ab`

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\\`