To determine the equivalent expression for [tex]\(4^2 \cdot 4^4\)[/tex], we need to use the properties of exponents. Specifically, when you multiply two numbers with the same base, you add their exponents.
1. Identify the base and the exponents in the given question:
[tex]\[
4^2 \cdot 4^4
\][/tex]
2. Since the base is the same (4), we add the exponents:
[tex]\[
2 + 4
\][/tex]
3. Performing the addition of the exponents gives us:
[tex]\[
2 + 4 = 6
\][/tex]
4. Therefore, the equivalent expression is:
[tex]\[
4^6
\][/tex]
So, the correct answer is:
[tex]\[
4^6
\][/tex]
