https://file.aiquickdraw.com/mathbot/file/1725973311081it84kpvd.jpg

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?

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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.

Which expression is equivalent to a^(1/3) + 2 / a^(2/3)?

Learn how to simplify the expression a^(1/3) + 2 / a^(2/3) by finding a common denominator and applying exponent rules. This step-by-step guide is suitable for students in Grades 9-12, covering key algebraic concepts and exponent manipulation.

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