To solve the problem in the image, we need to simplify the given expression:

$a^{1/3} + \frac{2}{a^{2/3}}$

First, let's identify the common denominator in this expression to combine the terms. The second term has a denominator of $a^{2/3}$, so we rewrite the first term $a^{1/3}$ with the same denominator:

$a^{1/3} = \frac{a^{1/3} \cdot a^{2/3}}{a^{2/3}} = \frac{a^{(1/3 + 2/3)}}{a^{2/3}} = \frac{a^{1}}{a^{2/3}} = \frac{a}{a^{2/3}}$

Now, the expression becomes:

$\frac{a}{a^{2/3}} + \frac{2}{a^{2/3}}$

Since both terms now have the same denominator, we can combine them:

$\frac{a + 2}{a^{2/3}}$

This matches option D in the multiple-choice answers.

Final Answer: D

Do you want more details or have any questions?

Here are five related questions for further practice:

1. Simplify $\frac{3}{a^{1/4}} + \frac{5}{a^{3/4}}$.
2. Simplify $x^{2/3} + \frac{4}{x^{1/3}}$.
3. Factor the expression $a^{2/3} + 2a^{1/3} + 1$.
4. Simplify $\frac{2x}{y^{2/3}} + \frac{3y}{x^{1/3}}$.
5. If $x = 2^{1/3}$, simplify $x + \frac{4}{x^2}$.

Tip: When adding or subtracting expressions with exponents, finding a common denominator often simplifies the process.