https://file.aiquickdraw.com/mathbot/file/1727786448671ylzzrz2h.jpg

The expression shown in the image is \(((-3)^2)^5\).

Let's break it down step by step:

1. **First, simplify the inside of the parentheses:**
   \[
   (-3)^2 = (-3) \times (-3) = 9
   \]
   So the expression becomes:
   \[
   9^5
   \]

2. **Now, calculate \(9^5\):**
   \[
   9^5 = 9 \times 9 \times 9 \times 9 \times 9 = 59,049
   \]

Thus, the value of the expression \(((-3)^2)^5\) is **59,049**.

Would you like a further breakdown or any additional details? Here are five related questions to extend your understanding:

1. What is the general rule for simplifying expressions with nested exponents?
2. How do negative bases behave under even and odd exponents?
3. What is the difference between \((-3)^2\) and \(-3^2\)?
4. How would the result change if the exponent were odd?
5. What are some common mistakes made when simplifying powers?

**Tip:** Always take care with parentheses when working with negative numbers raised to powers!

Learn how to simplify the expression ((-3)^2)^5. This step-by-step explanation covers key concepts in exponents, negative numbers, and the power of a power rule. Suitable for students in Grades 8-10.

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