To express \( x \) in the form of \( x^{-1} \), you're essentially applying the rule of exponents where raising a number to the power of \(-1\) gives its reciprocal.

So, the expression for \( x^{-1} \) is:

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

This means that when you raise \( x \) to the power of \(-1\), it is equivalent to taking the reciprocal of \( x \).

Would you like further details or examples on how this rule applies in different contexts?

Here are 5 related questions to deepen your understanding:
1. What happens when you raise a fraction to the power of \(-1\)?
2. How do you apply the exponent \(-1\) in a more complex algebraic expression?
3. What does \( (2x)^{-1} \) simplify to?
4. How would you apply the exponent \(-1\) to a square root function like \( \sqrt{x}^{-1} \)?
5. What is the graphical interpretation of \( x^{-1} \)?

**Tip:** Any nonzero number raised to the power of \(-1\) flips its value to its reciprocal!

Learn how to express x in the form of x^{-1} using exponent rules. This guide explains the concept of raising a number to the power of -1, the reciprocal theorem, and key formulas. Ideal for students in Grades 6-8.

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