Sure, let's simplify the expression [tex]\( b^5 \cdot b^4 \)[/tex] step by step.
When you multiply two exponential terms with the same base, you add their exponents. This is one of the properties of exponents. Here’s how it works:
1. Identify the base: Both terms have the same base [tex]\( b \)[/tex].
2. Add the exponents:
[tex]\[
b^5 \cdot b^4 = b^{5 + 4}
\][/tex]
3. Perform the addition:
[tex]\[
5 + 4 = 9
\][/tex]
4. Write the simplified form:
[tex]\[
b^5 \cdot b^4 = b^9
\][/tex]
Thus, the correct simplification of the expression [tex]\( b^5 \cdot b^4 \)[/tex] is [tex]\( b^9 \)[/tex].
So, the correct option is:
[tex]\[ \boxed{b^9} \][/tex]
