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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]
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