4. Вычислите: a) $$\frac{27^5 \cdot 3^2}{3^{16}} =$$ б) $$\frac{5^2 \cdot 6^3}{30^2} =$$

Решение: a) $$\frac{27^5 \cdot 3^2}{3^{16}} = \frac{(3^3)^5 \cdot 3^2}{3^{16}} = \frac{3^{15} \cdot 3^2}{3^{16}} = \frac{3^{15+2}}{3^{16}} = \frac{3^{17}}{3^{16}} = 3^{17-16} = 3^1 = 3$$ б) $$\frac{5^2 \cdot 6^3}{30^2} = \frac{5^2 \cdot 6^3}{(5 \cdot 6)^2} = \frac{5^2 \cdot 6^3}{5^2 \cdot 6^2} = \frac{6^3}{6^2} = 6^{3-2} = 6^1 = 6$$