Which expression is equivalent to $$ a^{1 / 3}+\frac{2}{a^{2 / 3}} $$ ? A. $$ \frac{a^{2 / 9}+2}{a^{2 / 3}} $$ B. $$ \frac{2}{a^{1 / 3}} $$ C. $$ \frac{a^{1 / 3}+2}{a^{2 / 3}} $$ D. $$ \frac{a+2}{a^{2 / 3}} $$ E. $$ \frac{a^{2 / 3}+2}{a} $$

Question

UpStudy AI · Accepted Answer

To determine which expression is equivalent to $$ a^{1/3} + \frac{2}{a^{2/3}} $$, let's simplify the original expression step by step.

**Original Expression:**
$$
a^{1/3} + \frac{2}{a^{2/3}}
$$

**Step 1: Find a Common Denominator**

The common denominator for the terms $$ a^{1/3} $$ and $$ \frac{2}{a^{2/3}} $$ is $$ a^{2/3} $$. Rewrite $$ a^{1/3} $$ with this denominator:
$$
a^{1/3} = \frac{a^{1/3} \cdot a^{2/3}}{a^{2/3}} = \frac{a^{1/3 + 2/3}}{a^{2/3}} = \frac{a}{a^{2/3}}
$$

**Step 2: Combine the Terms**
$$
\frac{a}{a^{2/3}} + \frac{2}{a^{2/3}} = \frac{a + 2}{a^{2/3}}
$$

**Final Simplified Form:**
$$
\frac{a + 2}{a^{2/3}}
$$

This matches option **D**.

**Answer:**  
**D.** $$ \frac{a+2}{a^{2 / 3}} $$
The equivalent expression is $$ \frac{a+2}{a^{2/3}} $$, which is option D.

Which expression is equivalent to \( a^{1 / 3}+\frac{2}{a^{2 / 3}} \) ? A. \( \frac{a^{2 / 9}+2}{a^{2 / 3}} \) B. \( \frac{2}{a^{1 / 3}} \) C. \( \frac{a^{1 / 3}+2}{a^{2 / 3}} \) D. \( \frac{a+2}{a^{2 / 3}} \) E. \( \frac{a^{2 / 3}+2}{a} \)

Solución de tutoría real

Responder

Solución

Beyond the Answer

preguntas relacionadas

Latest Algebra Questions