https://file.aiquickdraw.com/mathbot/file/1725932850669drnime5k.jpg

It seems the text extracted from the image is not fully accurate. Based on visual inspection of the image, the problem asks to simplify the expression:

\[
\frac{36x^5y^3z}{-9x^3y^2z^4}
\]

Let's go ahead and simplify this expression step-by-step.

### Step-by-Step Simplification:

1. **Numerical Coefficients**: 
   \[
   \frac{36}{-9} = -4
   \]

2. **Simplifying \( x \)-terms**: 
   \[
   \frac{x^5}{x^3} = x^{5-3} = x^2
   \]

3. **Simplifying \( y \)-terms**: 
   \[
   \frac{y^3}{y^2} = y^{3-2} = y
   \]

4. **Simplifying \( z \)-terms**: 
   \[
   \frac{z}{z^4} = z^{1-4} = z^{-3} = \frac{1}{z^3} \quad \text{(To avoid negative exponents, the z-term stays in the denominator.)}
   \]

### Final Simplified Expression:
\[
\frac{-4x^2y}{z^3}
\]

This is the fully simplified expression with no negative exponents.

Would you like any further explanation or have any questions about this simplification?

Here are some related questions you might find helpful:
1. How do you simplify expressions with negative exponents?
2. Can you explain the laws of exponents used in this problem?
3. How would you simplify an expression like \( \frac{x^a}{x^b} \) when \( a < b \)?
4. What happens when you have a zero exponent in a term?
5. How do fractional exponents relate to roots?

**Tip**: Always handle coefficients, variable bases, and exponents separately when simplifying algebraic expressions.

Completely simplify the following exponential expression: \( \frac{36x^5y^3z}{-9x^3y^2z^4} \) with no negative exponents.

Learn how to simplify the exponential expression \( \frac{36x^5y^3z}{-9x^3y^2z^4} \) step-by-step. This problem covers key algebraic concepts, including the laws of exponents and simplifying rational expressions. Suitable for students in Grades 9-11.

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