which expression is equivalent to $a^{1/3}+\frac{2}{a^{2/3}}$?\na. $\frac{a^{2/9}+2}{a^{2/3}}$\nb…

Explanation:

Step1: Find a common - denominator

The common denominator of $a^{1/3}$ and $\frac{2}{a^{2/3}}$ is $a^{2/3}$. Rewrite $a^{1/3}$ with the denominator $a^{2/3}$. Using the rule $x^m\cdot x^n=x^{m + n}$, we multiply the numerator and denominator of $a^{1/3}$ by $a^{1/3}$: $a^{1/3}=\frac{a^{1/3}\cdot a^{1/3}}{a^{1/3}}=\frac{a^{1/3 + 1/3}}{a^{2/3}}=\frac{a^{2/3}}{a^{2/3}}$.

Step2: Add the fractions

$a^{1/3}+\frac{2}{a^{2/3}}=\frac{a^{2/3}}{a^{2/3}}+\frac{2}{a^{2/3}}$. According to the rule $\frac{m}{n}+\frac{p}{n}=\frac{m + p}{n}$, we have $\frac{a^{2/3}+2}{a^{2/3}}$.

Answer:

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