To solve for the product of [tex]\(2^9 \cdot 2^{-2}\)[/tex], we can make use of the exponent rules. Specifically, when multiplying two expressions with the same base, we add their exponents.
Here, we have:
[tex]$
2^9 \cdot 2^{-2}
$[/tex]
Step 1: Add the exponents since the base (2) is the same.
[tex]\[9 + (-2) = 7\][/tex]
Step 2: Write the result in exponential form:
[tex]\[2^7\][/tex]
Thus, the product [tex]\(2^9 \cdot 2^{-2}\)[/tex] simplifies to [tex]\(2^7\)[/tex].
Now, to find the numerical value of [tex]\(2^7\)[/tex]:
[tex]\[2^7 = 128\][/tex]
So, the product is:
[tex]\[
\boxed{2^7 = 128}
\][/tex]
