The expression \(9^{-1}\) simplifies by using the rule of negative exponents, which states that \(a^{-n} = \frac{1}{a^n}\).

So, \(9^{-1}\) becomes:

\[
9^{-1} = \frac{1}{9}
\]

This does not equal \(1 - 9\), as the notation and meaning are different. \(1 - 9\) is simply the subtraction of 9 from 1, which equals \(-8\). However, \(9^{-1}\) refers to the reciprocal of 9, which simplifies to \(\frac{1}{9}\).

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### Related Questions
1. How does the rule of negative exponents work for other bases?
2. What happens if we apply a fractional exponent to 9, such as \(9^{\frac{1}{2}}\)?
3. How can we interpret expressions like \(9^{0}\)?
4. How does \(9^{-2}\) simplify?
5. Why is \(9^{-1}\) called the reciprocal of 9?

#### Tip:
To simplify expressions with negative exponents, always remember they represent reciprocals of the base raised to the positive exponent.

Learn how to simplify 9^-1 using the negative exponent rule, and understand why it does not equal 1-9. This problem focuses on exponents, reciprocal concepts, and the rule for negative exponents. Suitable for students in Grades 7-9.

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