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Evaluate [tex]\left(5^{-4}\right)\left(5^2\right)[/tex].

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

Answer :

We start with the expression

[tex]$$
(5^{-4})(5^2).
$$[/tex]

Since the bases are the same, we can add the exponents. That is, we use the property

[tex]$$
a^m \cdot a^n = a^{m+n}.
$$[/tex]

Thus,

[tex]$$
(5^{-4})(5^2) = 5^{-4+2} = 5^{-2}.
$$[/tex]

A negative exponent means taking the reciprocal of the base raised to the positive exponent:

[tex]$$
5^{-2} = \frac{1}{5^2}.
$$[/tex]

We then calculate [tex]$5^2$[/tex]:

[tex]$$
5^2 = 25.
$$[/tex]

So,

[tex]$$
\frac{1}{5^2} = \frac{1}{25}.
$$[/tex]

Therefore, the final answer is

[tex]$$
\frac{1}{25}.
$$[/tex]>

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