To simplify the expression [tex]\( f^4 \cdot f^8 \)[/tex], we can apply the rules of exponents.
The rule for multiplying exponential expressions with the same base is to add the exponents. This rule is written as follows:
[tex]\[ a^m \cdot a^n = a^{m+n} \][/tex]
In this case, the base is [tex]\( f \)[/tex], and we have two exponents: 4 and 8.
1. Identify the base and the exponents:
- Base: [tex]\( f \)[/tex]
- Exponents: 4 and 8
2. Add the exponents:
[tex]\[ 4 + 8 = 12 \][/tex]
3. Combine the base with the new exponent:
[tex]\[ f^{4+8} = f^{12} \][/tex]
Therefore, the correct simplification of the expression [tex]\( f^4 \cdot f^8 \)[/tex] is [tex]\( f^{12} \)[/tex].
So, the correct answer is:
[tex]\[ f^{12} \][/tex]
