Question

simplify
\\(\frac{n^2}{n^{\frac{1}{3}}}\\)
\\(\circ\\) a. \\(n^{\frac{2}{3}}\\)
\\(\circ\\) b. \\(n^{\frac{7}{3}}\\)
\\(\circ\\) c. \\(n^{\frac{5}{3}}\\)
\\(\circ\\) d. \\(n^3\\)

Explanation:

Step1: Apply exponent division rule

When dividing terms with the same base, subtract exponents: $\frac{n^a}{n^b}=n^{a-b}$. Here, $a=2$, $b=\frac{1}{3}$.
$\frac{n^2}{n^{\frac{1}{3}}}=n^{2-\frac{1}{3}}$

Step2: Compute exponent subtraction

Convert 2 to thirds to subtract: $2=\frac{6}{3}$.
$n^{\frac{6}{3}-\frac{1}{3}}=n^{\frac{5}{3}}$

Answer:

c. $n^{\frac{5}{3}}$