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To solve the equation \( 2^{(x+2)} = 4^2 \), we first recognize that \( 4 \) can be expressed as \( 2^2 \). Therefore, we can write \( 4^2 \) as follows:
\[ 4^2 = (2^2)^2 = 2^{2 \cdot 2} = 2^4 \]
Now we can rewrite the original equation:
\[ 2^{(x+2)} = 2^4 \]
Since the bases are the same, we can equate the exponents:
\[ x + 2 = 4 \]
Now, we solve for \( x \):
\[ x = 4 - 2 \] \[ x = 2 \]
Thus, the solution to the equation \( 2^{(x+2)} = 4^2 \) is
\[ \boxed{2} \]
It looks like there may have been a miscommunication regarding what you're looking for with "the missing value." If you are referring to the solution found in the previous equation, the missing value (solution for \( x \) in the equation \( 2^{(x+2)} = 4^2 \)) is \( x = 2 \).
If you meant something else or have a different context or a specific equation where a value is missing, please provide more details so I can assist you further!
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