Simplify the expression: $\frac{2}{3}x^4y^3 - \frac{1}{5}x^3y^2 + \frac{1}{4}xy - \frac{1}{5}xy^2$

1. Problem Description

Simplify the expression:

$\frac{2}{3}x^4y^3 - \frac{1}{5}x^3y^2 + \frac{1}{4}xy - \frac{1}{5}xy^2$

2. Solution Steps

The expression is $\frac{2}{3}x^4y^3 - \frac{1}{5}x^3y^2 + \frac{1}{4}xy - \frac{1}{5}xy^2$. We look for like terms that can be combined.

There are no like terms to combine. The terms are $\frac{2}{3}x^4y^3$, $-\frac{1}{5}x^3y^2$, $\frac{1}{4}xy$, and $-\frac{1}{5}xy^2$.

The exponents on the variables $x$ and $y$ are different in each term, so the terms are not like terms.

3. Final Answer

$\frac{2}{3}x^4y^3 - \frac{1}{5}x^3y^2 + \frac{1}{4}xy - \frac{1}{5}xy^2$