To find an equivalent expression to [tex]\(7 \cdot (1 + 0.09)^{2x}\)[/tex], let's break down the steps:
1. Simplify the expression inside the parentheses:
[tex]\[
1 + 0.09 = 1.09
\][/tex]
The expression now becomes [tex]\(7 \cdot (1.09)^{2x}\)[/tex].
2. Apply the exponentiation rule: [tex]\((a^m)^n = a^{mn}\)[/tex].
Here, we have [tex]\((1.09)^{2x}\)[/tex]. Using the exponentiation rule:
[tex]\[
(1.09)^{2x} = (1.09^2)^x
\][/tex]
3. Calculate [tex]\(1.09^2\)[/tex]:
[tex]\[
1.09^2 = 1.1881
\][/tex]
So, the expression simplifies to:
[tex]\[
7 \cdot (1.1881)^x
\][/tex]
Therefore, the equivalent expression to [tex]\(7 \cdot (1 + 0.09)^{2x}\)[/tex] is:
[tex]\[
\boxed{7 \cdot (1.1881)^x}
\][/tex]
