109. 1) 3/4 - (2/3)^(-1); 2) (1/27 * 125)^(-1/3); 3) 27^(2/3) + 7^(-2); 4) (0,01)^(-2) : 100^(-1/2); 5) ((64/81))^(-1/2) * (8/5)^(-1); 6) (2 * 10/27)^(-2/3) * (3/4)^2

Решение:

1. \( \frac{3}{4} - \left(\frac{2}{3}\right)^{-1} = \frac{3}{4} - \frac{3}{2} = \frac{3 - 6}{4} = -\frac{3}{4} \)
2. \( \left(\frac{1}{27} \cdot 125\right)^{-\frac{1}{3}} = \left(\frac{125}{27}\right)^{-\frac{1}{3}} = \left(\frac{5^3}{3^3}\right)^{-\frac{1}{3}} = \left(\left(\frac{5}{3}\right)^3\right)^{-\frac{1}{3}} = \left(\frac{5}{3}\right)^{-1} = \frac{3}{5} \)
3. \( 27^{\frac{2}{3}} + 7^{-2} = \left(3^3\right)^{\frac{2}{3}} + \frac{1}{7^2} = 3^2 + \frac{1}{49} = 9 + \frac{1}{49} = \frac{9 \cdot 49 + 1}{49} = \frac{441 + 1}{49} = \frac{442}{49} \)
4. \( (0,01)^{-2} : 100^{-\frac{1}{2}} = \left(10^{-2}\right)^{-2} : \left(10^2\right)^{-\frac{1}{2}} = 10^4 : 10^{-1} = 10^{4 - (-1)} = 10^5 = 100000 \)
5. \( \left(\frac{64}{81}\right)^{-\frac{1}{2}} \cdot \left(\frac{8}{5}\right)^{-1} = \left(\frac{8^2}{9^2}\right)^{-\frac{1}{2}} \cdot \frac{5}{8} = \left(\left(\frac{8}{9}\right)^2\right)^{-\frac{1}{2}} \cdot \frac{5}{8} = \left(\frac{8}{9}\right)^{-1} \cdot \frac{5}{8} = \frac{9}{8} \cdot \frac{5}{8} = \frac{45}{64} \)
6. \( \left(2 \cdot \frac{10}{27}\right)^{-\frac{2}{3}} \cdot \left(\frac{3}{4}\right)^2 = \left(\frac{20}{27}\right)^{-\frac{2}{3}} \cdot \frac{9}{16} = \left(\frac{3^3}{20}\right)^{\frac{2}{3}} \cdot \frac{9}{16} = \left(3^3\right)^{\frac{2}{3}} : \left(20\right)^{\frac{2}{3}} \cdot \frac{9}{16} = 3^2 \cdot \frac{1}{20^{\frac{2}{3}}} \cdot \frac{9}{16} = 9 \cdot \frac{1}{\sqrt[3]{400}} \cdot \frac{9}{16} \)

Ответ: 1) -3/4; 2) 3/5; 3) 442/49; 4) 100000; 5) 45/64; 6) 81 / (16 * ∛400)