Select the equivalent expression.
 
\[\dfrac{1}{9^{2}}=?\]
Choose 1 answer:
Choose 1 answer:
(Choice A)   
 
\[9^{^{\frac1{2}}}\]
A
 
\[9^{^{\frac1{2}}}\]
(Choice B)   
 
\[\dfrac{1^{2}}{9}\]
B
 
\[\dfrac{1^{2}}{9}\]
(Choice C)   
\[9^{-{2}}\]
C
\[9^{-{2}}\]

To determine the equivalent expression for \(\dfrac{1}{9^{2}}\), let's simplify it:

\[
\dfrac{1}{9^{2}} = 9^{-2}
\]

This is because when you have a reciprocal, the exponent becomes negative.

So, the correct answer is:

**Choice C:** \(9^{-2}\)

Would you like additional details or explanations on negative exponents?

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Here are five related questions you might find helpful:
1. How do we simplify expressions with negative exponents?
2. What does \(9^{\frac{1}{2}}\) represent in terms of radicals?
3. How does \(9^{-2}\) relate to the concept of reciprocals?
4. Why is \(1^{2}/9\) not equivalent to \(\dfrac{1}{9^{2}}\)?
5. Can we represent \(9^{-2}\) as a fraction with positive exponents?

**Tip:** Negative exponents signify taking the reciprocal of the base raised to the positive version of the exponent.

Select the equivalent expression. \(\dfrac{1}{9^{2}} = ?\) Choose 1 answer: (A) \(9^{\frac{1}{2}}\), (B) \(\dfrac{1^{2}}{9}\), (C) \(9^{-2}\)

Explore how to identify equivalent expressions involving negative exponents with the problem \(\dfrac{1}{9^{2}} = ?\). Learn key exponent rules, such as the reciprocal of a power, to understand why the answer is \(9^{-2}\). Suitable for Grades 7-8.

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