Simplify the product [3] 2 [4] 2 [12] 32 . - Vidyadip

Question

Simplify the product $\sqrt[3]{2}\times\sqrt[4]{2}\times\sqrt[12]{32}.$

✓

Answer

$\sqrt[3]{2}\times\sqrt[4]{2}\times\sqrt[12]{32}$$=2^\frac{1}{3}\times2^\frac{1}{4}\times32^\frac{1}{12}$
$=2^\frac{1}{3}\times2^\frac{1}{4}\times2^{5\times\frac{1}{12}}$
$=2^\frac{1}{3}\times2^\frac{1}{4}\times2^\frac{5}{12}$
$=2^{\frac{1}{3}+\frac{1}{4}+\frac{5}{12}}$
$=2^{\frac{4+3+5}{12}}$
$=2^\frac{12}{12}$
$=2$

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