To find the value of the algebraic expression [tex]\( 6x(y^2z) \)[/tex] given [tex]\( x = \frac{1}{2} \)[/tex], [tex]\( y = -1 \)[/tex], and [tex]\( z = 2 \)[/tex], let's evaluate it step by step:
1. Substitute the values into the expression:
[tex]\[
6 \cdot \left(\frac{1}{2}\right) \left((-1)^2 \cdot 2\right)
\][/tex]
2. Calculate [tex]\( (-1)^2 \)[/tex]:
[tex]\[
(-1)^2 = 1
\][/tex]
3. Substitute [tex]\( (-1)^2 = 1 \)[/tex] into the expression:
[tex]\[
6 \cdot \left(\frac{1}{2}\right) \left(1 \cdot 2\right)
\][/tex]
4. Calculate [tex]\( 1 \cdot 2 \)[/tex]:
[tex]\[
1 \cdot 2 = 2
\][/tex]
5. Substitute [tex]\( 2 \)[/tex] into the expression:
[tex]\[
6 \cdot \left(\frac{1}{2}\right) \cdot 2
\][/tex]
6. Calculate [tex]\( \left(\frac{1}{2}\right) \cdot 2 \)[/tex]:
[tex]\[
\left(\frac{1}{2}\right) \cdot 2 = 1
\][/tex]
7. Substitute [tex]\( 1 \)[/tex] into the expression:
[tex]\[
6 \cdot 1
\][/tex]
8. Calculate [tex]\( 6 \cdot 1 \)[/tex]:
[tex]\[
6 \cdot 1 = 6
\][/tex]
Therefore, the value of the algebraic expression [tex]\( 6x(y^2z) \)[/tex] with the given values for [tex]\( x \)[/tex], [tex]\( y \)[/tex], and [tex]\( z \)[/tex] is [tex]\( 6 \)[/tex].
So, the correct answer is:
D. [tex]\( 6 \)[/tex]
