Упр.58 ГДЗ Алимов 10-11 класс (Алгебра)

1. $$2^{\frac{4}{5}}\cdot 2^{\frac{11}{5}}=2^{\frac{4}{5}+\frac{11}{5}}=2^{\frac{15}{5}}=2^3=8$$

2. $$5^{\frac{2}{7}}\cdot 5^{\frac{5}{7}}=5^{\frac{2}{7}+\frac{5}{7}}=5^{\frac{7}{7}}=5^1=5$$

3. $$9^{\frac{2}{3}}:9^{\frac{1}{6}}=9^{\frac{2}{3}-\frac{1}{6}}=9^{\frac{4}{6}-\frac{1}{6}}=9^{\frac{3}{6}}=9^{\frac{1}{2}}=\sqrt{9}=3$$

4. $$4^{\frac{1}{3}}:4^{\frac{5}{6}}=4^{\frac{1}{3}-\frac{5}{6}}=4^{\frac{2}{6}-\frac{5}{6}}=4^{-\frac{3}{6}}=4^{-\frac{1}{2}}=\frac{1}{\sqrt{4}}=\frac{1}{2}$$

5. $$\left(8^{\frac{1}{2}}\right)^{-4}=8^{-\frac{4}{2}}=8^{-2}=\frac{1}{8^2}=\frac{1}{64}$$

Ответ

$$1)\ 8;\quad 2)\ 5;\quad 3)\ 3;\quad 4)\ \frac{1}{2};\quad 5)\ \frac{1}{64}$$