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The expression to simplify is \((10^{-4})^{-1}\).

### Step-by-step solution:

1. Apply the exponent rule \((a^m)^n = a^{m \cdot n}\) to simplify:
   \[
   (10^{-4})^{-1} = 10^{-4 \cdot (-1)} = 10^4
   \]

Thus, \((10^{-4})^{-1} = 10^4\).

### Answer:
The correct option is \(10^4\).

Would you like further details, or have any questions on this?

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Here are 5 related questions to help deepen your understanding:
1. What happens if the exponent inside the parentheses is positive instead of negative?
2. How do exponent rules apply when dealing with negative bases?
3. What is the difference between \((10^2)^3\) and \(10^{2 \cdot 3}\)?
4. How would you simplify an expression like \((10^{-4})^2\)?
5. Can you explain how fractional exponents relate to radicals?

**Tip**: When raising a power to another power, always multiply the exponents, even if they are negative or fractional!

Which expression is equivalent to (10^{-4})^{-1}?

Learn how to simplify the expression (10^{-4})^{-1} by applying the exponent rule. This problem covers key algebraic concepts involving exponents. Suitable for Grade 8 students.

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