https://file.aiquickdraw.com/mathbot/file/1725503864106fdbkoi0f.jpg

The expression provided is:

\[
\frac{1}{-3n^{-5}}
\]

### Step 1: Eliminate the negative exponent
To eliminate the negative exponent, recall the rule: 
\[
a^{-n} = \frac{1}{a^n}
\]

Applying this rule to \(n^{-5}\), we get:
\[
n^{-5} = \frac{1}{n^5}
\]

### Step 2: Substitute the expression
Now, substitute \(\frac{1}{n^5}\) back into the original expression:
\[
\frac{1}{-3n^{-5}} = \frac{1}{-3 \cdot \frac{1}{n^5}} = \frac{1}{- \frac{3}{n^5}} 
\]

### Step 3: Simplify the fraction
Dividing by a fraction is the same as multiplying by its reciprocal:
\[
\frac{1}{- \frac{3}{n^5}} = \frac{n^5}{-3}
\]

### Final Answer:
\[
\frac{n^5}{-3} \quad \text{or} \quad -\frac{n^5}{3}
\]

This is the simplified expression without using a negative exponent.

Would you like further details or have any questions about the process? 

Here are some related questions to consider:
1. How do we handle more complex negative exponents?
2. Can the properties of exponents be extended to fractional exponents?
3. How do negative exponents interact with multiplication and division?
4. What happens if both the base and the exponent are negative?
5. How does exponentiation behave when applied to polynomial expressions?

**Tip:** Always remember that a negative exponent in a fraction can be rewritten by flipping the base to the denominator or numerator, as appropriate.

Rewrite the expression without using a negative exponent. Simplify your answer as much as possible. 
\( \frac{1}{-3n^{-5}} \)

Learn how to simplify the expression \( \frac{1}{-3n^{-5}} \) by eliminating negative exponents. This problem demonstrates how to apply the laws of exponents and provides a step-by-step solution suitable for students in Grades 9-10.

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