The problem asks us to factor out the common factor $5a$ from the expression $25a^{7/3} - 35a^{9/5}$. We need to find the expression that, when multiplied by $5a$, gives $25a^{7/3} - 35a^{9/5}$.

1. Problem Description

The problem asks us to factor out the common factor $5a$ from the expression $25a^{7/3} - 35a^{9/5}$. We need to find the expression that, when multiplied by $5a$, gives $25a^{7/3} - 35a^{9/5}$.

2. Solution Steps

First, we can rewrite the expression as

$25a^{7/3} - 35a^{9/5} = 5(5)a^{7/3} - 5(7)a^{9/5}$.

Now, we want to factor out $5a$.

$25a^{7/3} - 35a^{9/5} = 5a (\frac{25a^{7/3}}{5a} - \frac{35a^{9/5}}{5a})$

$= 5a (5a^{7/3 - 1} - 7a^{9/5 - 1})$

$= 5a (5a^{7/3 - 3/3} - 7a^{9/5 - 5/5})$

$= 5a (5a^{4/3} - 7a^{4/5})$

Therefore, the expression inside the parentheses is $5a^{4/3} - 7a^{4/5}$.

3. Final Answer

$5a^{4/3} - 7a^{4/5}$