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].
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].
