Упростите: a) $$b^{-\frac{1}{3}}b^{\frac{1}{2}}$$; б) $$\frac{a^2 \cdot a^{\frac{3}{4}}}{a^{-\frac{1}{4}}}$$

а) $$b^{-\frac{1}{3}}b^{\frac{1}{2}} = b^{-\frac{1}{3} + \frac{1}{2}} = b^{\frac{-2+3}{6}} = b^{\frac{1}{6}}$$

б) $$\frac{a^2 \cdot a^{\frac{3}{4}}}{a^{-\frac{1}{4}}} = a^{2+\frac{3}{4}-(-\frac{1}{4})} = a^{2+\frac{3}{4}+\frac{1}{4}} = a^{2+\frac{4}{4}} = a^{2+1} = a^3$$