To simplify the given expression:

$\frac{2x^4y^{-4}z^{-3}}{3x^2y^{-3}z^4}$

We simplify each term separately:

1. Simplify the coefficients: $\frac{2}{3}$

2. Simplify the $x$-terms: $x^{4 - 2} = x^2$

3. Simplify the $y$-terms: $y^{-4 - (-3)} = y^{-4 + 3} = y^{-1}$

4. Simplify the $z$-terms: $z^{-3 - 4} = z^{-7}$

Combine all simplified terms:

$\frac{2}{3}x^2y^{-1}z^{-7}$

To write with positive exponents:

$\frac{2x^2}{3yz^7}$

Let me know if you'd like further explanation or examples!

Related Questions:

1. How do you simplify expressions with negative exponents?
2. How can this expression be written in terms of roots?
3. What are the rules for multiplying and dividing exponents?
4. How do fractional exponents fit into this?
5. What is the best way to factor similar expressions?

Tip:

Always simplify exponents term by term for clarity and avoid mistakes!