Question

Which expression is equivalent to 4 6/3 2

Answer 1

9514 1404 393

Answer:

  C

Step-by-step explanation:

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

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