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2015-09-30T11:27:18+08:00

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 \sqrt{2} = 2 ^{1/2}

 \sqrt[3]{2}  =  2^{1/3}

Transform the expressions to similar terms.  The rule is in multiplying and dividing radicals, they must have the same index

Find the LCD of the fractional exponents 1/2 and 1/3, then re-write the radical with the same index.

LCD of 1/2 and 1/3 is 6:

2 ^{3/6} =  \sqrt[6]{2 ^{3} } =  \sqrt[6]{(2)(2)(2)} =  \sqrt[6]{8}

 2^{2/6} = \sqrt[6]{ 2^{2} } =  \sqrt[6]{ 2^{2} } =  \sqrt[6]{(2)(2)} = \sqrt[6]{4}

Dive the radicals:
 \frac{ \sqrt[6]{8} }{ \sqrt[6]{4} } =  \sqrt[6]{2}

 \sqrt[6]{2} is the final answer.

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