Упр.513 ГДЗ Колягин Ткачёва 10 класс (Алгебра)

1. $$\left(\frac{1}{27}\cdot125^{-1}\right)^{-1/3}$$
2. $$\left(0{,}01\right)^{-2}:100^{-1/2}$$
3. $$\left(\frac{2\cdot10}{27}\right)^{-2/3}\cdot\left(\frac{3}{4}\right)^2$$

1. $$\left(\frac{1}{27}\cdot 125^{-1}\right)^{-\frac13}$$
   $$=\left(3^{-3}\cdot 5^{-3}\right)^{-\frac13}$$
   $$=\left((3\cdot 5)^{-3}\right)^{-\frac13}=(15)^{1}=15.$$

2. $$(0{,}01)^{-2}:100^{-\frac12}$$
   $$=(10^{-2})^{-2}: (10^2)^{-\frac12}$$
   $$=10^4:10^{-1}=10^5=100000.$$

3. $$\left(2\frac{10}{27}\right)^{-\frac23}\cdot \left(\frac34\right)^2$$
   $$=\left(\frac{64}{27}\right)^{-\frac23}\cdot \frac{9}{16}$$
   $$=\left(\frac{4^3}{3^3}\right)^{-\frac23}\cdot \frac{9}{16}$$
   $$=\left(\frac43\right)^{-2}\cdot \frac{9}{16}$$
   $$=\left(\frac34\right)^2\cdot \frac{9}{16}=\frac{9}{16}\cdot \frac{9}{16}=\frac{81}{256}.$$

Ответ

1) $$15$$; 2) $$100000$$; 3) $$\frac{81}{256}$$.