The problem asks us to divide the expression $2a^{9/5}b^4 - a^{7/3}b^4 - a^3b^2$ by $5ab$.

1. Problem Description

The problem asks us to divide the expression $2a^{9/5}b^4 - a^{7/3}b^4 - a^3b^2$ by $5ab$.

2. Solution Steps

We can rewrite the expression as:

$\frac{2a^{9/5}b^4 - a^{7/3}b^4 - a^3b^2}{5ab}$.

We can split this fraction into three separate fractions:

$\frac{2a^{9/5}b^4}{5ab} - \frac{a^{7/3}b^4}{5ab} - \frac{a^3b^2}{5ab}$

We can simplify each fraction using the property $\frac{a^m}{a^n} = a^{m-n}$ and $\frac{b^m}{b^n} = b^{m-n}$.

For the first term:

$\frac{2a^{9/5}b^4}{5ab} = \frac{2}{5}a^{9/5 - 1}b^{4-1} = \frac{2}{5}a^{9/5 - 5/5}b^3 = \frac{2}{5}a^{4/5}b^3$

For the second term:

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

For the third term:

$\frac{a^3b^2}{5ab} = \frac{1}{5}a^{3-1}b^{2-1} = \frac{1}{5}a^2b$

Combining these three simplified terms:

$\frac{2}{5}a^{4/5}b^3 - \frac{1}{5}a^{4/3}b^3 - \frac{1}{5}a^2b$

3. Final Answer

$\frac{2}{5}a^{4/5}b^3 - \frac{1}{5}a^{4/3}b^3 - \frac{1}{5}a^2b$