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.