To solve the problem [tex]\( 2^9 \cdot 2^{-2} \)[/tex], we will use the properties of exponents. Specifically, we will use the property that states:
[tex]\[
a^m \cdot a^n = a^{m+n}
\][/tex]
In this case, our base [tex]\( a \)[/tex] is [tex]\( 2 \)[/tex], and the exponents are [tex]\( 9 \)[/tex] and [tex]\( -2 \)[/tex].
First, we add the exponents together:
[tex]\[
9 + (-2) = 7
\][/tex]
This gives us:
[tex]\[
2^{9 + (-2)} = 2^7
\][/tex]
Therefore, the product of [tex]\( 2^9 \)[/tex] and [tex]\( 2^{-2} \)[/tex] is:
[tex]\[
2^7
\][/tex]
So the answer is:
[tex]\[
2^7
\][/tex]
