Упр.388 ГДЗ Никольский Потапов 9 класс (Алгебра)

• а) $$a^{-1/2}:\sqrt{a}$$; б) $$z^{2/3}:\sqrt[5]{z^2}$$; в) $$\sqrt[4]{m}:m^{-1/2}$$; г) $$\sqrt[3]{a}:a^{-1/6}$$

Используем свойства степеней и корней:

$$\sqrt{a}=a^{\frac12}, \quad \sqrt[5]{z^2}=z^{\frac25}, \quad \sqrt[4]{m}=m^{\frac14}, \quad \sqrt[3]{a}=a^{\frac13}.$$

1. $$a^{-\frac12}:\sqrt{a}=a^{-\frac12}:a^{\frac12}=a^{-\frac12-\frac12}=a^{-1}=\frac1a.$$

2. $$z^{\frac23}:\sqrt[5]{z^2}=z^{\frac23}:z^{\frac25}=z^{\frac23-\frac25}=z^{\frac{10}{15}-\frac{6}{15}}=z^{\frac4{15}}.$$

3. $$\sqrt[4]{m}:m^{-\frac12}=m^{\frac14}:m^{-\frac12}=m^{\frac14-(-\frac12)}=m^{\frac14+\frac12}=m^{\frac34}.$$

4. $$\sqrt[3]{a}:a^{-\frac16}=a^{\frac13}:a^{-\frac16}=a^{\frac13-(-\frac16)}=a^{\frac13+\frac16}=a^{\frac12}.$$

Ответ

$$\frac1a;\ \ z^{\frac4{15}};\ \ m^{\frac34};\ \ a^{\frac12}.$$