4. Расположите числа в порядке возрастания: 1) 2^{-3/4}; 2; 1/2; 2^{2/3}; 2^{-4/3}; 2) (1/3)^2; (1/3)^{-1/2}; 9^{-1/3}; 3^4; (1/9)^{-3/2}; 3) 24; (3/2)^4; (-3)^4; (-3/4)^{-4}; (9/25)^2; 4) 3^3; (-2)^3; (1/27)^{-2}; (2/3)^{-3}; 2^6.

Сравним значения выражений.

1. \(2^{-4/3}\approx0.397\), \(\frac12=0.5\), \(2^{-3/4}\approx0.595\), \(2^{2/3}\approx1.587\), \(2=2\).

   Ответ: \(2^{-4/3};\ \frac12;\ 2^{-3/4};\ 2^{2/3};\ 2\).

2. \(\left(\frac13\right)^2=\frac19\), \(9^{-1/3}=\frac1{\sqrt[3]{9}}\approx0.481\), \(\left(\frac13\right)^{-1/2}=\sqrt3\approx1.732\), \(3^4=81\), \(\left(\frac19\right)^{-3/2}=9^{3/2}=27\).

   Ответ: \(\left(\frac13\right)^2;\ 9^{-1/3};\ \left(\frac13\right)^{-1/2};\ \left(\frac19\right)^{-3/2};\ 3^4\).

3. \(\left(\frac{9}{25}\right)^2=0.1296\), \(\left(-\frac34\right)^{-4}=\left(\frac43\right)^4\approx3.16\), \(\left(\frac32\right)^4=5.0625\), \(24=24\), \((-3)^4=81\).

   Ответ: \(\left(\frac{9}{25}\right)^2;\ \left(-\frac34\right)^{-4};\ \left(\frac32\right)^4;\ 24;\ (-3)^4\).

4. \((-2)^3=-8\), \(\left(\frac23\right)^{-3}=\left(\frac32\right)^3=3.375\), \(3^3=27\), \(2^6=64\), \(\left(\frac1{27}\right)^{-2}=27^2=729\).

   Ответ: \((-2)^3;\ \left(\frac23\right)^{-3};\ 3^3;\ 2^6;\ \left(\frac1{27}\right)^{-2}\).