The expression you've written, \(-b^{-4}\), involves a negative sign and a power of a negative exponent. Let's break it down step by step:

1. \( b^{-4} \) means the reciprocal of \( b^4 \), which is written as:

\[
b^{-4} = \frac{1}{b^4}
\]

2. The negative sign outside makes the expression:

\[
-b^{-4} = -\frac{1}{b^4}
\]

Thus, the simplified form of \(-b^{-4}\) is:

\[
-\frac{1}{b^4}
\]

If \(b \neq 0\), the expression is valid.

Would you like more details on negative exponents or how to handle them in equations?

### Related Questions:
1. What happens if \(b = 0\) in the expression \(b^{-4}\)?
2. How does the expression change if the exponent were positive (e.g., \(b^4\))?
3. How do we differentiate expressions with negative exponents?
4. What are some real-life applications of negative exponents?
5. How does this expression behave when substituting specific values for \(b\)?

**Tip:** Negative exponents represent the inverse of a number raised to a positive power.

Explore the concept of negative exponents through the example -b^-4. This solution breaks down how negative exponents work and simplifies the expression step by step. Key topics include algebraic manipulation of exponents and the reciprocal property. Suitable for students in Grades 8-10.

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