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