Let's solve the problem step-by-step:
1. We are given [tex]\( x = 2 \)[/tex] and [tex]\( z = 2 \)[/tex].
2. First, we need to determine the exponent by adding 2 to [tex]\( x \)[/tex]:
[tex]\[
x + 2 = 2 + 2 = 4
\][/tex]
3. Now, we need to raise [tex]\( z \)[/tex] to the power of the result from step 2:
[tex]\[
z^{x+2} = 2^4
\][/tex]
4. We know that raising 2 to the power of 4 means multiplying 2 by itself 4 times:
[tex]\[
2^4 = 2 \times 2 \times 2 \times 2 = 16
\][/tex]
Therefore, the result of [tex]\( z^{x+2} \)[/tex] when [tex]\( x = 2 \)[/tex] and [tex]\( z = 2 \)[/tex] is [tex]\( 16 \)[/tex]. The correct answer is [tex]\( \boxed{16} \)[/tex].
