Question

Simplify and express as positive indice:

(xy)^(m-n).(yz)^(n-l).(zx)^(l-m)

Answer 1

(xy)^(m-n).(yz)^(n-l).(zx)^(l-m)

Step 1: Expand powers

(xy)^m−n = x^m−ny^m−n, (yz)^n−l = y^n−lz^n−l, (zx)^l−m = z^l−mx^l−m.

Step 2: Combine powers of x, y, and z

1. For x: x^m-n.x^l-m = x^l-n
2. For y: y^m-n.y^n-1 = y^m-1
3. For z: z^n-1.z^l-m = z^n-m

x^l-n.y^m-l.z^n-m