To express [tex]\(5^{20}\)[/tex] as a power of [tex]\(25\)[/tex], we can follow these steps:
1. Recognize the relationship between the bases:
- Notice that [tex]\(25\)[/tex] can be expressed as a power of [tex]\(5\)[/tex]. Specifically, [tex]\(25 = 5^2\)[/tex].
2. Rewrite the given expression:
- We start with [tex]\(5^{20}\)[/tex]. We want to rewrite this expression using [tex]\(25\)[/tex] as the base.
- Since [tex]\(25 = 5^2\)[/tex], we can substitute [tex]\(5^2\)[/tex] for [tex]\(25\)[/tex] in the expression.
3. Rewrite [tex]\(5^{20}\)[/tex]:
- Substitute [tex]\(25\)[/tex] for [tex]\(5^2\)[/tex] in [tex]\(5^{20}\)[/tex]:
[tex]\[
5^{20} = (5^2)^{10}
\][/tex]
- Notice that [tex]\((5^2)^{10}\)[/tex] is the same as [tex]\(25^{10}\)[/tex], because when a power is raised to another power, you multiply the exponents:
[tex]\[
(5^2)^{10} = 25^{10}
\][/tex]
4. Conclusion:
- Thus, [tex]\(5^{20}\)[/tex] expressed as a power of [tex]\(25\)[/tex] is:
[tex]\[
5^{20} = 25^{10}
\][/tex]
So, [tex]\(5^{20}\)[/tex] can be rewritten as [tex]\(25^{10}\)[/tex].
