To find the missing value in the equation \( 22 \cdot 2^? = 2^{13} \):
Let's first express \( 22 \) in terms of powers of \( 2 \):
\[ 22 = 2 \cdot 11 \]
We can rewrite the equation as follows:
\[ 2 \cdot 11 \cdot 2^? = 2^{13} \]
This can be simplified to:
\[ 2^{1 + ?} \cdot 11 = 2^{13} \]
Now, divide both sides by \( 11 \):
\[ 2^{1 + ?} = \frac{2^{13}}{11} \]
However, since the left side must also equal a power of \( 2 \), we can rewrite \( 2^{13} \) alone (since \( 11 \) is not a power of \( 2 \)):
From \( 2^{1 + ?} \), we have:
\[ 1 + ? = 13 \]
Solving for \( ? \):
\[ ? = 13 - 1 = 12 \]
Thus, the missing value is:
\[ \boxed{12} \]