College

Which choice is equivalent to the expression below?

[tex]5^{-2}[/tex]

A. [tex]\frac{1}{25}[/tex]
B. -10
C. [tex]\frac{1}{10}[/tex]
D. [tex]-\frac{1}{25}[/tex]

Answer :

To solve the expression [tex]\(5^{-2}\)[/tex], we need to understand what a negative exponent indicates. A negative exponent means that you take the reciprocal of the base raised to the positive of that exponent. In simpler terms:

[tex]\(5^{-2}\)[/tex] is the same as [tex]\(\frac{1}{5^2}\)[/tex].

Now, let's calculate [tex]\(5^2\)[/tex]:

[tex]\[5^2 = 5 \times 5 = 25.\][/tex]

So, [tex]\(\frac{1}{5^2} = \frac{1}{25}\)[/tex].

This means that the expression [tex]\(5^{-2}\)[/tex] is equivalent to:

A. [tex]\(\frac{1}{25}\)[/tex].

Therefore, the correct choice is A. [tex]\(\frac{1}{25}\)[/tex].