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Answer :
We start with the expression
[tex]$$
5^{-2}.
$$[/tex]
Recall that a negative exponent indicates the reciprocal of the base raised to the positive exponent. That is, for any nonzero number [tex]$a$[/tex] and positive integer [tex]$n$[/tex], we have
[tex]$$
a^{-n} = \frac{1}{a^n}.
$$[/tex]
Applying this rule to [tex]$5^{-2}$[/tex] gives:
[tex]$$
5^{-2} = \frac{1}{5^2}.
$$[/tex]
Next, compute [tex]$5^2$[/tex]:
[tex]$$
5^2 = 25.
$$[/tex]
So, the expression becomes:
[tex]$$
5^{-2} = \frac{1}{25}.
$$[/tex]
Thus, the equivalent expression is [tex]$\frac{1}{25}$[/tex], which corresponds to choice D.
[tex]$$
5^{-2}.
$$[/tex]
Recall that a negative exponent indicates the reciprocal of the base raised to the positive exponent. That is, for any nonzero number [tex]$a$[/tex] and positive integer [tex]$n$[/tex], we have
[tex]$$
a^{-n} = \frac{1}{a^n}.
$$[/tex]
Applying this rule to [tex]$5^{-2}$[/tex] gives:
[tex]$$
5^{-2} = \frac{1}{5^2}.
$$[/tex]
Next, compute [tex]$5^2$[/tex]:
[tex]$$
5^2 = 25.
$$[/tex]
So, the expression becomes:
[tex]$$
5^{-2} = \frac{1}{25}.
$$[/tex]
Thus, the equivalent expression is [tex]$\frac{1}{25}$[/tex], which corresponds to choice D.
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