Упр.18.22 ГДЗ Мерзляк 10 класс Базовый уровень (Алгебра)

1) ((5^(3/4)·2^(3/4))/(2^(-1/4)·10))^4;
2) ((7^(9/4)·3^(7/4))/(3^(1/4)·7^(3/4))^(2/3).

1. $$\left(\frac{5^{3/4}\cdot 2^{3/4}}{2^{-1/4}\cdot 10}\right)^4$$
   Представим $$10$$ как $$5\cdot 2$$:
   $$\left(\frac{5^{3/4}\cdot 2^{3/4}}{2^{-1/4}\cdot 5\cdot 2}\right)^4$$
   Тогда
   $$\left(\frac{5^{3/4}\cdot 2^{3/4}}{5\cdot 2^{3/4}}\right)^4 = \left(\frac{5^{3/4}}{5}\right)^4 = \left(5^{-1/4}\right)^4 = 5^{-1} = \frac{1}{5}.$$

2. $$\left(\frac{7^{9/4}\cdot 3^{7/4}}{3^{1/4}\cdot 7^{3/4}}\right)^{2/3}$$
   Упростим дробь:
   $$\left(7^{9/4-3/4}\cdot 3^{7/4-1/4}\right)^{2/3} = \left(7^{6/4}\cdot 3^{6/4}\right)^{2/3} = \left(7^{3/2}\cdot 3^{3/2}\right)^{2/3}.$$
   Далее:
   $$\left((7\cdot 3)^{3/2}\right)^{2/3} = 21^{(3/2)\cdot(2/3)} = 21.$$

Ответ

1) $$\frac{1}{5}$$; 2) $$21$$.