1. **State the problem:** Simplify the expression $$\left(\frac{z}{\pi x}\right)^{-1} \times \left(\frac{z}{\pi x}\right)^{-2}$$. 2. **Recall the exponent rule:** When multiplying powers with the same base, add the exponents: $$a^m \times a^n = a^{m+n}$$. 3. **Apply the rule:** $$\left(\frac{z}{\pi x}\right)^{-1} \times \left(\frac{z}{\pi x}\right)^{-2} = \left(\frac{z}{\pi x}\right)^{-1 + (-2)} = \left(\frac{z}{\pi x}\right)^{-3}$$. 4. **Rewrite negative exponent:** $$\left(\frac{z}{\pi x}\right)^{-3} = \frac{1}{\left(\frac{z}{\pi x}\right)^3}$$. 5. **Simplify the denominator:** $$\frac{1}{\left(\frac{z}{\pi x}\right)^3} = \frac{1}{\frac{z^3}{(\pi x)^3}} = \frac{(\pi x)^3}{z^3}$$. 6. **Final simplified form:** $$y = \frac{(\pi x)^3}{z^3}$$. --- 1. **State the problem:** Simplify the infinite continued fraction: $$y = \frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{1}{1+\cdots}}}}$$. 2. **Recognize the pattern:** Let the infinite continued fraction be $y$ itself, so: $$y = \frac{1}{1 + y}$$. 3. **Solve for $y$:** Multiply both sides by $1 + y$: $$y(1 + y) = 1$$. 4. **Expand:** $$y + y^2 = 1$$. 5. **Rewrite as quadratic:** $$y^2 + y - 1 = 0$$. 6. **Use quadratic formula:** $$y = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{-1 \pm \sqrt{1^2 - 4 \times 1 \times (-1)}}{2 \times 1} = \frac{-1 \pm \sqrt{1 + 4}}{2} = \frac{-1 \pm \sqrt{5}}{2}$$. 7. **Choose positive root (since $y$ is positive):** $$y = \frac{-1 + \sqrt{5}}{2}$$. --- **Final answers:** $$\boxed{y = \frac{(\pi x)^3}{z^3}}$$ and $$\boxed{y = \frac{-1 + \sqrt{5}}{2}}$$