Answered

Looking for reliable answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Get accurate and detailed answers to your questions from a dedicated community of experts on our Q&A platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

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. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.