What is the value of the algebraic expression if [tex][tex]$x=\frac{1}{2}, y=-1$[/tex][/tex], and [tex][tex]$z=2$[/tex][/tex]?

[tex]
6 x\left(y^2 z\right)
[/tex]

A. -12
B. -6
C. 1
D. 6



Answer :

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]