https://file.aiquickdraw.com/mathbot/file/1726192346566fw7lsnz6.jpg

Let's go over the multiplication of monomials based on the provided image.

### Directions: 
Find each product and express the final answer using exponents.

### Solutions:
1. **Problem 17:**  
   \[ 3^2 \times 3^4 \]  
   Use the property of exponents: \( a^m \times a^n = a^{m+n} \)  
   \[ 3^2 \times 3^4 = 3^{2+4} = 3^6 \]

2. **Problem 18:**  
   \[ (-5)^2 \times (-5)^1 \]  
   Apply the same rule for exponents:  
   \[ (-5)^2 \times (-5)^1 = (-5)^{2+1} = (-5)^3 \]

3. **Problem 19:**  
   \[ 7^2 \times 7^3 \]  
   \[ 7^{2+3} = 7^5 \]

4. **Problem 20:**  
   \[ 12 \times 12^2 \]  
   \[ 12^1 \times 12^2 = 12^{1+2} = 12^3 \]

5. **Problem 21:**  
   \[ 5^7 \times 5^3 \]  
   \[ 5^{7+3} = 5^{10} \]  
   You correctly marked this as \( 5^{10} \).

6. **Problem 22:**  
   \[ (-4)^5 \times (-4)^4 \]  
   \[ (-4)^{5+4} = (-4)^9 \]

7. **Problem 23:**  
   \[ x^{12} \times x^3 \]  
   \[ x^{12+3} = x^{15} \]

8. **Problem 24:**  
   \[ y^0 \times (y^4) \]  
   Anything to the power of 0 is 1:  
   \[ y^0 \times y^4 = 1 \times y^4 = y^4 \]

9. **Problem 25:**  
   \[ p \times p^4 \]  
   \[ p^1 \times p^4 = p^{1+4} = p^5 \]

10. **Problem 26:**  
    \[ xy^i \times y^5 \]  
    Combine the powers of \( y \):  
    \[ xy^i \times y^5 = xy^{i+5} \]

11. **Problem 27:**  
    \[ m^n \times m^5 \times m^3 \]  
    Add the exponents:  
    \[ m^{n+5+3} = m^{n+8} \]

12. **Problem 28:**  
    \[ xy \times x^3 y^3 \]  
    Add the exponents for \( x \) and \( y \):  
    \[ x^1 \times x^3 = x^{1+3} = x^4 \]  
    \[ y^1 \times y^3 = y^{1+3} = y^4 \]  
    So, the final answer is:  
    \[ x^4 y^4 \]

Would you like to go over the remaining problems or have any specific questions on these? 

Here are some related questions to expand your understanding:

1. How would you simplify an expression like \( 2^3 \times 2^5 \)?
2. What is the general rule for dividing monomials with the same base?
3. How do you handle exponents when multiplying numbers with negative bases?
4. How do you simplify an expression like \( a^0 \times a^n \)?
5. What happens if you multiply two different variables, like \( x^2 \times y^3 \)?

**Tip:** When multiplying monomials, always look for bases that are the same to simplify the expression using the exponent rules!

Explore how to multiply monomials by applying exponent rules. This worksheet includes problems like 3^2 * 3^4 and (-5)^2 * (-5). Learn the key steps to simplify expressions using exponent rules for grades 8-10.

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