To simplify the expression \((\frac{1}{16x^{-8}})^{-1}\), we can follow these steps:

### Step 1: Apply the negative exponent rule
The negative exponent rule states that \((a^m)^{-1} = a^{-m}\), so we can rewrite the expression by flipping the fraction:

\[
(\frac{1}{16x^{-8}})^{-1} = 16x^{-8}
\]

### Step 2: Simplify the exponents
We are left with \(16x^{-8}\). To simplify this further, we can deal with the exponent of \(x\):

\[
x^{-8} = \frac{1}{x^8}
\]

Thus, the expression becomes:

\[
16 \cdot \frac{1}{x^8} = \frac{16}{x^8}
\]

### Final Answer:
\[
\frac{16}{x^8}
\]

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

### Related Questions:
1. How do you simplify expressions with multiple variables and negative exponents?
2. What happens when both the numerator and denominator have negative exponents?
3. Can you explain the rule for multiplying exponents with the same base?
4. How do you handle fractional exponents in simplification problems?
5. What are the steps to simplify expressions involving radicals and exponents?

**Tip:** Always remember to apply the negative exponent rule first when simplifying expressions.

Learn how to simplify the expression (1/16x^-8)^-1 step by step using the negative exponent rule and laws of exponents. This detailed solution is suitable for students in Grades 8-10 and covers key concepts in algebra and exponents.

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