[tex] \sqrt{2} = 2 ^{1/2} [/tex]
[tex] \sqrt[3]{2} = 2^{1/3} [/tex]
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:
[tex]2 ^{3/6} = \sqrt[6]{2 ^{3} } = \sqrt[6]{(2)(2)(2)} = \sqrt[6]{8} [/tex]
[tex] 2^{2/6} = \sqrt[6]{ 2^{2} } = \sqrt[6]{ 2^{2} } = \sqrt[6]{(2)(2)} = \sqrt[6]{4} [/tex]
Dive the radicals:
[tex] \frac{ \sqrt[6]{8} }{ \sqrt[6]{4} } = \sqrt[6]{2} [/tex]
[tex] \sqrt[6]{2} [/tex] is the final answer.
