You have to check which of the following expressions is the rational exponent expression of third root of 4n, or mathematically, [tex] \sqrt[3]{4n} . [/tex] Consider all cases:
A. [tex] (4n)^3=4^3\cdot n^3=64n^3\neq\sqrt[3]{4n} . [/tex]
B. [tex] 3n^4\neq \sqrt[3]{4n} . [/tex]
C. quantity of 4n to the one third power is [tex] (4n)^{\frac{1}{3} }=\sqrt[3]{4n} [/tex] (by the definition of rational power).
D. 4 times n to the one third power is [tex] 4\cdot n^{\frac{1}{3} }=4\sqrt[3]{n}\neq \sqrt[3]{4n} . [/tex]
Answer: correct choice is C.
