https://r2.erweima.ai/mathbot/image/1726770018034bdbdsuze.jpg

The mathematical expression in the image is:

\[
\left( \frac{1}{b^{-2}} \right)^3
\]

To simplify this, let's follow these steps:

1. First, recall that \( b^{-2} \) can be written as \( \frac{1}{b^2} \).
   So, \( \frac{1}{b^{-2}} = b^2 \).

2. Now, apply the exponent \( 3 \) to the result:
   \[
   (b^2)^3 = b^{2 \cdot 3} = b^6
   \]

Therefore, the simplified expression is:

\[
b^6
\]

Let me know if you'd like more details or if you have any further questions!

Here are five related questions to expand on this concept:

1. What are the rules for simplifying expressions with negative exponents?
2. How do you simplify expressions involving multiple exponents, like \( (b^m)^n \)?
3. What happens when you multiply terms with the same base but different exponents?
4. How would you handle a fraction raised to a negative power?
5. What is the general rule for simplifying a product raised to a power?

**Tip:** When simplifying exponents, always remember that negative exponents indicate reciprocal relationships, and multiplying powers with the same base involves adding the exponents.

Learn how to simplify the expression (1 / b^(-2))^3. This example covers essential algebraic rules, including exponent laws and negative exponents. Follow a step-by-step approach suitable for students in Grades 9-10.

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