The power 92

Question

is equivalent to 81
. What is the value of 9−2
?(1 point)
Responses

19
1 ninth

−81
negative 81

181
1 over 81

−9

Answer 1

To solve for \( 9^{-2} \), we can use the definition of negative exponents. Specifically, \( a^{-n} = \frac{1}{a^n} \).

So,

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

Next, calculate \( 9^2 \):

\[ 9^2 = 81 \]

Now substitute back:

\[ 9^{-2} = \frac{1}{81} \]

This means the value of \( 9^{-2} \) is \( \frac{1}{81} \), which can also be written as "1 over 81."

Therefore, the correct response is:

1 over 81.