https://file.aiquickdraw.com/mathbot/file/1726696049699vj55erqs.jpg

The problem in the image asks to find the degree of the polynomial:

\[
x^4 y^9 - 9x^{13} y^9 + 36x^9 y^9
\]

### To determine the degree of the polynomial:

1. **Find the degree of each term:**
   - The degree of a term is the sum of the exponents of all variables.
   - For the term \( x^4 y^9 \), the degree is \( 4 + 9 = 13 \).
   - For the term \( -9x^{13} y^9 \), the degree is \( 13 + 9 = 22 \).
   - For the term \( 36x^9 y^9 \), the degree is \( 9 + 9 = 18 \).

2. **The degree of the polynomial** is the highest degree among all the terms. 
   - The degrees are: 13, 22, and 18.
   - Therefore, the degree of the polynomial is \( \boxed{22} \).

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Here are 5 related questions for practice:

1. What is the degree of the polynomial \( 3x^5 y^7 - 2x^3 y^6 + x^2 y^8 \)?
2. How do you find the degree of a polynomial with multiple variables?
3. If you add or subtract two polynomials, how does that affect the degree?
4. What is the degree of the polynomial \( 5x^{10} + 4x^8 + 2x^6 \)?
5. How can the degree of a polynomial help in solving algebraic equations?

**Tip:** The degree of a polynomial tells you how many roots (real or complex) it can have and gives insight into the polynomial's end behavior.

Degree of the polynomial x^4 y^9 - 9x^{13} y^9 + 36x^9 y^9

Learn how to determine the degree of the polynomial x^4 y^9 - 9x^{13} y^9 + 36x^9 y^9. This problem explains how to find the degree by summing the exponents of the variables in each term. Suitable for high school students studying algebra.

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