To find the largest possible value of the expression (x/y)​z², we need to consider the maximum and minimum values of each variable x, y, and z.

Given:

• x, y, and z are chosen from the numbers -3, 1/2​, and 2.

First, let's find the maximum and minimum values of x/y​:

• If x=−3 and y=21​, then x/y=−6.
• If x=2 and y=21​, then x/y​=4.

So, the minimum value of x/y​ is -6, and the maximum value is 4.

Now, let's consider the maximum and minimum values of z²:

• If z=−3, then z²=9.
• If z=2, then z²=4.

So, the minimum value of z² is 4, and the maximum value is 9.

To maximize the expression (x/y)z², we need to choose the maximum value of x/y​ and the maximum value of z²:

Max value=Max(x/y)×Max(z²)

=4×9

=36