Problem: The product of 43\sqrt[3]{4}34 and 84\sqrt[4]{8}48 equals
Answer Choices:
A. 127\sqrt[7]{12}712
B. 21272 \sqrt[7]{12}2712
C. 327\sqrt[7]{32}732
D. 3212\sqrt[12]{32}1232
E. 232122 \sqrt[12]{32}21232 Solution:
4384=(22)13(23)14=21712=23212\sqrt[3]{4} \quad \sqrt[4]{8}=\left(2^{2}\right)^{\dfrac{1}{3}}\left(2^{3}\right)^{\dfrac{1}{4}}=2^{\dfrac{17}{12}}=2 \sqrt[12]{32}3448=(22)31(23)41=21217=21232.