Show that:`(a^(x-y))^(x+y).(a^(y-z))^(y+z).(x^(z-x))^(z+x)=1`

Explanation

To prove that \((a^{(x-y)})^{(x+y)} \cdot (a^{(y-z)})^{(y+z)} \cdot (a^{(z-x)})^{(z+x)} = 1\), we will simplify the expression step by step.

### Step 1: Rewrite the expression using the power of a power property
Using the property \((a^m)^n = a^{m \cdot n}\), we can rewrite each term in the expression:

\[ (a^{(x-y)})^{(x+y)} = a^{(x-y)(x+y)} \]
...