1. **State the problem:** Simplify the expression $$\left(\frac{z}{\pi x}\right)^{1-2} \times \left(\frac{z}{\pi x}\right)^{2-1}$$. 2. **Apply the exponent subtraction:** Calculate the exponents inside the parentheses: $$1-2 = -1$$ $$2-1 = 1$$ So the expression becomes: $$\left(\frac{z}{\pi x}\right)^{-1} \times \left(\frac{z}{\pi x}\right)^{1}$$ 3. **Use the product of powers rule:** When multiplying powers with the same base, add the exponents: $$a^m \times a^n = a^{m+n}$$ Applying this: $$\left(\frac{z}{\pi x}\right)^{-1 + 1} = \left(\frac{z}{\pi x}\right)^0$$ 4. **Simplify any expression to the zero power:** Any nonzero base raised to the zero power equals 1: $$\left(\frac{z}{\pi x}\right)^0 = 1$$ **Final answer:** $$1$$