The problem is to factor out the common factor of $3a$ from the expression $6a^{7/3} - 21a^{5/4}$.

1. Problem Description

The problem is to factor out the common factor of $3a$ from the expression $6a^{7/3} - 21a^{5/4}$.

2. Solution Steps

First, we rewrite the expression as:

$6a^{7/3} - 21a^{5/4} = 3a(\text{something})$

We need to find what "something" is. We divide each term by $3a$. Remember that $a = a^1$.

$\frac{6a^{7/3}}{3a} = \frac{6}{3} a^{7/3 - 1} = 2a^{7/3 - 3/3} = 2a^{4/3}$

$\frac{-21a^{5/4}}{3a} = \frac{-21}{3} a^{5/4 - 1} = -7a^{5/4 - 4/4} = -7a^{1/4}$

Therefore,

$6a^{7/3} - 21a^{5/4} = 3a(2a^{4/3} - 7a^{1/4})$

3. Final Answer

$2a^{4/3} - 7a^{1/4}$