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Let's go through the questions from the image.

### **Exercise 13**
- The problem asks to determine whether a number is positive or negative based on two given cases.

1. **If \( n \) is a positive even number, then \((-55)^n\) is:**  
   When an odd number is raised to an even power, the result is positive, because multiplying an odd number an even number of times results in a positive number.  
   Therefore, \( (-55)^n \) is **positive**.

2. **If \( n \) is a positive odd number, then \( (-72)^n \) is:**  
   When a negative number is raised to an odd power, the result remains negative.  
   Therefore, \( (-72)^n \) is **negative**.

### **Exercise 14**
- Josie says that \( (-15) \times (-(-15)) = -15^2 \). Is she correct? How do you know?

To check Josie's statement:

1. \( (-(-15)) = 15 \), because negating a negative number gives a positive number.
2. So, \( (-15) \times 15 = -225 \).
3. Now, \( -15^2 = -(15^2) = -225 \).

Thus, Josie's statement is correct, because both sides evaluate to \(-225\).

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Would you like further details or clarifications?

Here are 5 related questions to explore:
1. What happens when a negative number is raised to an odd power?
2. How does raising an even number to any power affect the sign of the result?
3. What is the difference between \( -a^n \) and \( (-a)^n \)?
4. How do parentheses affect the outcome of powers of negative numbers?
5. Why is \( (-a)^n \) positive when \( n \) is even and negative when \( n \) is odd?

**Tip:** When dealing with exponents, always be cautious with the placement of parentheses around negative numbers, as it can change the result.

Fill in the blanks indicating whether the number is positive or negative. Josie says that (-15) x -(-15) = -15^2. Is she correct?

Learn how to determine whether numbers raised to powers are positive or negative and verify Josie's statement regarding multiplying negative numbers. Suitable for students in Grades 8-10.

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