Question

Which expression is equivalent to 4 6/3 2

Answer 1

9514 1404 393

Answer:

C

Explanation:

A root with a given index is the same as a fractional power with that index as the denominator.

`\frac{\sqrt[4]{6}}{\sqrt[3]{2}}=6^{(1)/(4)}2^{-(1)/(3)}=\sqrt[12]{(6^{(1)/(4)}2^{-(1)/(3)})^(12)}=\sqrt[12]{6^32^(-4)}\\\\=\sqrt[12]{6^32^82^(-12)}=\frac{\sqrt[12]{6^32^8}}{2}=\boxed{\frac{\sqrt[12]{55296}}{2}}`