Question

Which of the following is the rational exponent expression of third root of 4 n? A) (4n)3

Answer 1

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. $(4n)^3=4^3\cdot n^3=64n^3\neq\sqrt[3]{4n} .$

B. $3n^4\neq \sqrt[3]{4n} .$

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 $4\cdot n^{\frac{1}{3} }=4\sqrt[3]{n}\neq \sqrt[3]{4n} .$

Answer: correct choice is C.

Answer 2

The answer to the question above should be letter "C. quantity of 4 n to the one-third power". This means that the radicand is the product of 4 and n. This product is raised to the power 1/3. Mathematically,
                                   (4n)^1/3