https://file.aiquickdraw.com/mathbot/file/1726097488141cfxdcsje.jpg

Let's go through the problems one by one.

### Part A: 
**Expression:** \( 2^3 \times 2^8 \)

1. **What is the common base?**  
   The common base is \( 2 \), since both terms share the base \( 2 \).

2. **What is the sum of the exponents?**  
   We add the exponents using the *Product of Powers Property*:  
   \( 3 + 8 = 11 \).

3. **What power is equivalent to the multiplication expression?**  
   The equivalent expression is:  
   \[
   2^{3+8} = 2^{11}
   \]

---

### Part B: 
**Expression:** \( 5^9 \div 5^6 \)

4. **What is the common base?**  
   The common base is \( 5 \).

5. **What is the difference of the exponents?**  
   We subtract the exponents using the *Quotient of Powers Property*:  
   \( 9 - 6 = 3 \).

6. **What power is equivalent to the division expression?**  
   The equivalent expression is:  
   \[
   5^{9-6} = 5^3
   \]

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Would you like a more detailed explanation for any of these steps? Here are 5 related questions to expand on this concept:

1. What is the base in the expression \( 10^5 \times 10^3 \)?
2. If you have \( 3^4 \times 3^7 \), what would the equivalent power be?
3. How would you simplify \( 4^8 \div 4^5 \)?
4. Can you apply the product of powers property to \( 7^2 \times 2^3 \)?
5. How does the quotient of powers property work when dividing powers of the same base with equal exponents?

**Tip:** Always ensure that the base of the numbers is the same before applying the product or quotient of powers properties.

Use the properties of exponents to write an equivalent expression for 2^3 * 2^8 and 5^9 ÷ 5^6.

Learn how to simplify expressions using the properties of exponents. This tutorial covers the product of powers property and quotient of powers property through detailed examples. Suitable for Grades 6-8 students.

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