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.
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.
