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------------------------------------------------ What is the value of this expression [tex]$\frac{1}{5^{-5}}$[/tex]?

A. 25
B. [tex]$\frac{1}{25}$[/tex]
C. 3125
D. [tex]$\frac{1}{3125}$[/tex]

Answer :

Sure, let's find the value of the expression [tex]\(\frac{1}{5^{-5}}\)[/tex].

1. Understand the Expression:
- We are given [tex]\(\frac{1}{5^{-5}}\)[/tex].
- A negative exponent means reciprocal, so [tex]\(5^{-5}\)[/tex] is [tex]\(\frac{1}{5^5}\)[/tex].

2. Simplify the Expression:
- Using the property of exponents, [tex]\(\frac{1}{5^{-5}}\)[/tex] can be rewritten using the rule that [tex]\(a^{-b} = \frac{1}{a^b}\)[/tex].

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

3. Calculate [tex]\(5^5\)[/tex]:
- Now we need to calculate the value of [tex]\(5^5\)[/tex].
- [tex]\(5^5\)[/tex] means multiply 5 by itself 5 times:

[tex]\[
5^5 = 5 \times 5 \times 5 \times 5 \times 5 = 3125
\][/tex]

Therefore, the value of the expression [tex]\(\frac{1}{5^{-5}}\)[/tex] is [tex]\(\boxed{3125}\)[/tex].