Answered

Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Get immediate answers to your questions from a wide network of experienced professionals on our Q&A platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

Which expression is equivalent to [tex]$9^{-2}$[/tex]?

A. [tex]$-81$[/tex]
B. [tex][tex]$-18$[/tex][/tex]
C. [tex]$\frac{1}{81}$[/tex]
D. [tex]$\frac{1}{18}$[/tex]

Sagot :

GinnyAnswer
To determine which expression is equivalent to [tex]\( 9^{-2} \)[/tex], we need to recall the rules of exponents. Specifically, when dealing with a negative exponent, the expression [tex]\( a^{-b} \)[/tex] is equivalent to [tex]\( \frac{1}{a^b} \)[/tex].

Given [tex]\( 9^{-2} \)[/tex]:

1. Convert the negative exponent to a reciprocal format:
[tex]\[ 9^{-2} = \frac{1}{9^2} \][/tex]

2. Calculate [tex]\( 9^2 \)[/tex]:
[tex]\[ 9^2 = 9 \times 9 = 81 \][/tex]

3. Place the result in the reciprocal expression:
[tex]\[ 9^{-2} = \frac{1}{81} \][/tex]

Therefore, the expression [tex]\( \frac{1}{81} \)[/tex] is equivalent to [tex]\( 9^{-2} \)[/tex].

The correct answer is:
[tex]\(\frac{1}{81}\)[/tex]
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.