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].
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].
