Question

which expression is equivalent to $5^{-2}$?
select the correct choice.
a $-25$
b $-10$
c $\frac{1}{25}$
d $\frac{1}{10}$

Explanation:

Step1: Recall the negative exponent rule

The rule for negative exponents is \( a^{-n} = \frac{1}{a^{n}} \) for any non - zero number \( a \) and positive integer \( n \).

Step2: Apply the rule to \( 5^{-2} \)

Using the rule \( a^{-n}=\frac{1}{a^{n}} \) with \( a = 5 \) and \( n=2 \), we have \( 5^{-2}=\frac{1}{5^{2}} \).

Step3: Calculate \( 5^{2} \)

We know that \( 5^{2}=5\times5 = 25 \).

Step4: Substitute the value of \( 5^{2} \)

Substituting \( 5^{2}=25 \) into \( \frac{1}{5^{2}} \), we get \( \frac{1}{25} \).

Answer:

C. \(\frac{1}{25}\)