To determine which expression is equal to [tex]\(5^4 \cdot 5^5\)[/tex], we need to use the properties of exponents.
When we multiply powers that have the same base, we add the exponents. In this case, both terms have the base of 5:
[tex]\[5^4 \cdot 5^5\][/tex]
Let's add the exponents:
[tex]\[5^4 \cdot 5^5 = 5^{4 + 5}\][/tex]
Adding the exponents:
[tex]\[5^{4 + 5} = 5^9\][/tex]
Therefore, the expression equal to [tex]\(5^4 \cdot 5^5\)[/tex] is:
[tex]\[
\boxed{5^9}
\][/tex]
This shows that none of the options [tex]$5^{12}$[/tex], [tex]$5^4$[/tex], [tex]$5^2$[/tex], or [tex]$5^{-4}$[/tex] are correct, since the correct exponent should be [tex]\(9\)[/tex].
