Question

the product
$\sqrt[3]{2} \sqrt[4]{2} \sqrt[12]{32}$
​

Answer 1

Step-by-step explanation:

$\sqrt[3]{2} \sqrt[4]{2} \sqrt[12]{32} \\ \\ = {2}^{ \frac{1}{3} } \times {2}^{ \frac{1}{4} } \times { 32}^{ \frac{1}{12} } \\ \\ = {2}^{ \frac{1}{3} } \times {2}^{ \frac{1}{4} } \times {2}^{5 \times \frac{1}{12} } \\ \\ = {2}^{ (\frac{1}{3} + \frac{1}{4} + \frac{5}{12}) } \\ \\ = {2}^{( \frac{4 + 3 + 5}{12} )} \\ \\ = {2}^{ (\frac{12}{12} )} \\ \\ = {2}^{1} \\ \\ = 2$

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