High School

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

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

Answer :

To find the value of the expression [tex]\(\frac{1}{5^{-5}}\)[/tex], let's work through the steps one by one:

1. Understand the expression:

The given expression is [tex]\(\frac{1}{5^{-5}}\)[/tex].

2. Simplify the expression using properties of exponents:

Recall that any number raised to a negative exponent can be rewritten as the reciprocal of the number raised to the corresponding positive exponent. Therefore, [tex]\(5^{-5}\)[/tex] can be rewritten as [tex]\(\frac{1}{5^5}\)[/tex].

So, the original expression can be rewritten as:
[tex]\[
\frac{1}{5^{-5}} = \frac{1}{\frac{1}{5^5}}
\][/tex]

3. Simplify the fraction:

When you divide 1 by a fraction, it is equivalent to multiplying by the reciprocal of that fraction. Therefore:
[tex]\[
\frac{1}{\frac{1}{5^5}} = 5^5
\][/tex]

4. Calculate [tex]\(5^5\)[/tex]:

Find the value of [tex]\(5^5\)[/tex]:
[tex]\[
5^5 = 5 \times 5 \times 5 \times 5 \times 5 = 3125
\][/tex]

5. Conclusion:

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

So, the correct answer is [tex]\(3125\)[/tex].