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

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

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

Answer

Explanation:

Step1: Find a common - denominator

The given expression is $\frac{a^{2/3}}{b^{1/3}}+\frac{b^{2/3}}{a^{1/3}}$. The common denominator of $b^{1/3}$ and $a^{1/3}$ is $a^{1/3}b^{1/3}$.

Step2: Rewrite each fraction with the common denominator

$\frac{a^{2/3}}{b^{1/3}}\times\frac{a^{1/3}}{a^{1/3}}=\frac{a^{2/3 + 1/3}}{a^{1/3}b^{1/3}}=\frac{a}{a^{1/3}b^{1/3}}$ and $\frac{b^{2/3}}{a^{1/3}}\times\frac{b^{1/3}}{b^{1/3}}=\frac{b^{2/3+1/3}}{a^{1/3}b^{1/3}}=\frac{b}{a^{1/3}b^{1/3}}$.

Step3: Add the fractions

$\frac{a}{a^{1/3}b^{1/3}}+\frac{b}{a^{1/3}b^{1/3}}=\frac{a + b}{a^{1/3}b^{1/3}}$.

Answer:

A. $\frac{a + b}{a^{1/3}b^{1/3}}$