Sure! Let's express [tex]\( 5^{20} \)[/tex] as a power of 25. Follow these steps:
1. Understand the relationship between 5 and 25:
Note that [tex]\( 25 \)[/tex] can be written as [tex]\( 5^2 \)[/tex].
2. Rewrite [tex]\( 5^{20} \)[/tex] using the relationship:
Since [tex]\( 25 = 5^2 \)[/tex], we can rewrite [tex]\( 5^{20} \)[/tex] in terms of [tex]\( 25 \)[/tex]:
[tex]\[
5^{20} = (5^2)^{10}
\][/tex]
3. Simplify the expression:
Using the property of exponents that [tex]\((a^m)^n = a^{mn}\)[/tex], we have:
[tex]\[
(5^2)^{10} = 25^{10}
\][/tex]
So, [tex]\( 5^{20} \)[/tex] expressed as a power of 25 is [tex]\( 25^{10} \)[/tex].
To confirm, let's check the numerical result:
[tex]\[
25^{10} = 95367431640625
\][/tex]
Therefore, [tex]\( 5^{20} \)[/tex] written as a power of 25 is [tex]\( 25^{10} \)[/tex].
