College

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

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

Answer :

To solve the expression [tex]\(\frac{1}{5^{-5}}\)[/tex], let's break it down step by step:

1. Understanding the expression: The expression [tex]\(\frac{1}{5^{-5}}\)[/tex] can be rewritten using the property of exponents that states [tex]\(a^{-b} = \frac{1}{a^b}\)[/tex].

2. Convert the negative exponent: We have [tex]\(5^{-5}\)[/tex], which means [tex]\(\frac{1}{5^5}\)[/tex].

3. Simplify the expression: The expression [tex]\(\frac{1}{5^{-5}}\)[/tex] is equivalent to flipping the fraction. So, [tex]\(\frac{1}{5^{-5}} = 5^5\)[/tex].

4. Calculate [tex]\(5^5\)[/tex]: Now, calculate [tex]\(5^5\)[/tex].
[tex]\[
5^5 = 5 \times 5 \times 5 \times 5 \times 5
\][/tex]

First, calculate [tex]\(5 \times 5 = 25\)[/tex].

Then, [tex]\(25 \times 5 = 125\)[/tex].

Next, [tex]\(125 \times 5 = 625\)[/tex].

Finally, [tex]\(625 \times 5 = 3125\)[/tex].

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

So, the correct answer is 3125.