Упр.28.184 ГДЗ Мерзляк 11 класс Углубленный уровень (Алгебра)

1) (b(b^4)^(1/5))^(1/4); 2) (c(c^2)^(1/7))^(1/3); 3) (a^2 (a^2)^(1/5))^(1/6).

1. $$\left(b\left(b^4\right)^{\frac15}\right)^{\frac14}=\left(b\cdot b^{\frac45}\right)^{\frac14}=\left(b^{\frac95}\right)^{\frac14}=b^{\frac9{20}}=\sqrt[20]{b^9}.$$
2. $$\left(c\left(c^2\right)^{\frac17}\right)^{\frac13}=\left(c\cdot c^{\frac27}\right)^{\frac13}=\left(c^{\frac97}\right)^{\frac13}=c^{\frac37}=\sqrt[7]{c^3}.$$
3. $$\left(a^2\left(a^2\right)^{\frac15}\right)^{\frac16}=\left(a^2\cdot a^{\frac25}\right)^{\frac16}=\left(a^{\frac{12}5}\right)^{\frac16}=a^{\frac25}=\sqrt[5]{a^2}.$$

Ответ

1) $$\sqrt[20]{b^9}$$; 2) $$\sqrt[7]{c^3}$$; 3) $$\sqrt[5]{a^2}$$.