To simplify \((2^{-1})^{-3}\):

1. First, apply the power of a power rule \((a^m)^n = a^{m \cdot n}\):
   \[
   (2^{-1})^{-3} = 2^{-1 \cdot (-3)} = 2^3
   \]
   
2. Now simplify \(2^3\):
   \[
   2^3 = 8
   \]

Thus, \((2^{-1})^{-3} = 8\).

Would you like further details on exponent rules or have any questions?

Here are 5 related questions:
1. What is \((3^{-1})^{-4}\)?
2. How do you simplify \((5^{-2})^3\)?
3. Can you explain the power of a power rule?
4. What happens if the base is negative, like \((-2^{-1})^{-3}\)?
5. What is the result of \((2^2)^{-3}\)?

**Tip:** Always simplify step-by-step when dealing with powers to avoid mistakes.

Learn how to simplify the expression (2^-1)^-3 using the power of a power rule. This detailed solution breaks down each step, applying exponent rules and simplifying expressions. Perfect for students in Grades 6-8.

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