To determine which expression is equal to [tex]\(5^4 \cdot 5^8\)[/tex], we can use the properties of exponents. Specifically, when multiplying expressions with the same base, we add the exponents:
[tex]\[
a^m \cdot a^n = a^{m+n}
\][/tex]
Given this property, we can apply it to our specific case:
[tex]\[
5^4 \cdot 5^8
\][/tex]
Here, the base [tex]\(a\)[/tex] is 5, [tex]\(m\)[/tex] is 4, and [tex]\(n\)[/tex] is 8. Using the property:
[tex]\[
5^4 \cdot 5^8 = 5^{4+8}
\][/tex]
Now, add the exponents:
[tex]\[
4 + 8 = 12
\][/tex]
So, the expression simplifies to:
[tex]\[
5^{12}
\][/tex]
Thus, the expression [tex]\(5^4 \cdot 5^8\)[/tex] is equal to [tex]\(5^{12}\)[/tex]. The correct answer is:
[tex]\[
\boxed{5^{12}}
\][/tex]
