Let's solve the problem step-by-step.
1. First, let’s define the variables [tex]\( f \)[/tex] and [tex]\( g \)[/tex]. For this problem, let's consider [tex]\( f = 2 \)[/tex] and [tex]\( g = 3 \)[/tex].
2. We are asked to find the value of [tex]\((f \cdot g)^9\)[/tex].
3. Substitute the values of [tex]\( f \)[/tex] and [tex]\( g \)[/tex] into the expression:
[tex]\[
(f \cdot g)^9 = (2 \cdot 3)^9
\][/tex]
4. Calculate the product inside the parentheses first:
[tex]\[
2 \cdot 3 = 6
\][/tex]
5. Now we need to raise this product to the 9th power:
[tex]\[
6^9
\][/tex]
6. When you calculate [tex]\( 6^9 \)[/tex], you obtain the result:
[tex]\[
6^9 = 10077696
\][/tex]
Therefore, the product [tex]\((f \cdot g)^9\)[/tex] when [tex]\( f = 2 \)[/tex] and [tex]\( g = 3 \)[/tex] is [tex]\(\boxed{10077696}\)[/tex].
