Answer :
To solve the expression [tex]$(-5)^{-2}$[/tex], let's break it down step-by-step.
1. Understand Negative Exponents: A negative exponent means you take the reciprocal of the base. For example, [tex]\( a^{-b} = \frac{1}{a^b} \)[/tex].
2. Apply the Negative Exponent Rule: For the expression [tex]\((-5)^{-2}\)[/tex]:
[tex]\[
(-5)^{-2} = \frac{1}{(-5)^2}
\][/tex]
3. Calculate the Positive Exponent: Now, calculate [tex]\((-5)^2\)[/tex]:
[tex]\[
(-5) \times (-5) = 25
\][/tex]
4. Find the Reciprocal: Since we have [tex]\(\frac{1}{(-5)^2}\)[/tex], now substitute the value we found:
[tex]\[
\frac{1}{25}
\][/tex]
So, [tex]\((-5)^{-2}\)[/tex] is equivalent to [tex]\(\frac{1}{25}\)[/tex].
Therefore, the correct choice is [tex]\( C. \frac{1}{25} \)[/tex].
1. Understand Negative Exponents: A negative exponent means you take the reciprocal of the base. For example, [tex]\( a^{-b} = \frac{1}{a^b} \)[/tex].
2. Apply the Negative Exponent Rule: For the expression [tex]\((-5)^{-2}\)[/tex]:
[tex]\[
(-5)^{-2} = \frac{1}{(-5)^2}
\][/tex]
3. Calculate the Positive Exponent: Now, calculate [tex]\((-5)^2\)[/tex]:
[tex]\[
(-5) \times (-5) = 25
\][/tex]
4. Find the Reciprocal: Since we have [tex]\(\frac{1}{(-5)^2}\)[/tex], now substitute the value we found:
[tex]\[
\frac{1}{25}
\][/tex]
So, [tex]\((-5)^{-2}\)[/tex] is equivalent to [tex]\(\frac{1}{25}\)[/tex].
Therefore, the correct choice is [tex]\( C. \frac{1}{25} \)[/tex].