**Solution:**

To find the value of the expression x^q-r * y^r-p * z^p-q, we need to use the given information that p, q, and r are in arithmetic progression (AP) and x, y, and z are in geometric progression (GP).

Let's first express p, q, and r in terms of their common difference in the AP.

**Arithmetic Progression (AP):**

The general form of an arithmetic progression is given by: a, a + d, a + 2d, a + 3d, ...

Where 'a' is the first term and 'd' is the common difference.

Given that p, q, and r are in AP, we can express them as:

p = a + 0d
q = a + 1d
r = a + 2d

Now, let's express x, y, and z in terms of their common ratio in the GP.

**Geometric Progression (GP):**

The general form of a geometric progression is given by: a, ar, ar^2, ar^3, ...

Where 'a' is the first term and 'r' is the common ratio.

Given that x, y, and z are in GP, we can express them as:

x = a * r^0 = a
y = a * r^1 = ar
z = a * r^2

Now, let's substitute the expressions for p, q, and r in terms of 'a' and 'd', and x, y, and z in terms of 'a' and 'r' into the given expression:

x^q-r * y^r-p * z^p-q

Substituting the values:
(a)^(a + d - r) * (ar)^(a + 2d - p) * (a * r^2)^(a + d - a)

Simplifying the exponents:
(a)^(a + d - r) * (ar)^(a + 2d - p) * (a^2 * r^2)^(d)

Expanding the exponents:
(a)^(a + d - r) * (a^(a + 2d - p) * r^(a + 2d - p)) * (a^(2d) * r^(2d))

Combining the terms with the same base:
a^(2a + 3d - r - p) * r^(3d - p)

Therefore, the expression x^q-r * y^r-p * z^p-q simplifies to:
a^(2a + 3d - r - p) * r^(3d - p)

X^q-r × y^r-p ×z^p-q
=(1^2-3) × (2^3-1) × (4^1-2)
=(1^-1) × (2^2) × (4^-1)
=1/1 × 4 × 1/4
=1