37.18. a) $$x^{\frac{1}{2}} \cdot \sqrt{x}$$; б) $$y^{\frac{7}{3}} \cdot \sqrt[3]{y^2}$$; в) $$z^{\frac{3}{4}} \cdot \sqrt[4]{z}$$; г) $$\sqrt[4]{c^3} \cdot c^{\frac{1}{4}}$$.

a) $$x^{\frac{1}{2}} \cdot \sqrt{x} = x^{\frac{1}{2}} \cdot x^{\frac{1}{2}} = x^{\frac{1}{2} + \frac{1}{2}} = x^1 = x$$. б) $$y^{\frac{7}{3}} \cdot \sqrt[3]{y^2} = y^{\frac{7}{3}} \cdot y^{\frac{2}{3}} = y^{\frac{7}{3} + \frac{2}{3}} = y^{\frac{9}{3}} = y^3$$. в) $$z^{\frac{3}{4}} \cdot \sqrt[4]{z} = z^{\frac{3}{4}} \cdot z^{\frac{1}{4}} = z^{\frac{3}{4} + \frac{1}{4}} = z^{\frac{4}{4}} = z^1 = z$$. г) $$\sqrt[4]{c^3} \cdot c^{\frac{1}{4}} = c^{\frac{3}{4}} \cdot c^{\frac{1}{4}} = c^{\frac{3}{4} + \frac{1}{4}} = c^{\frac{4}{4}} = c^1 = c$$. Ответ: а) $$x$$, б) $$y^3$$, в) $$z$$, г) $$c$$