1.159. Вычислите: a) (2/3)^-2 + (4/7)^-1 ; b) (1/6)^-2 + 6^-3 : 36^-2 - 0,6^0 ; б) (2^-1 - 3^-1 * 6)^-1 ; г) (2^-2 * 5^2 - 25) / 10^-2 ; 1.162. Найдите значение выражения (-1/4)^-10 * 64^-3 - 0,2^4 * 25^-2 + 0,125^-1 .

1.159.

а)

1. \( \left(\frac{2}{3}\right)^{-2} = \left(\frac{3}{2}\right)^{2} = \frac{9}{4} \)
2. \( \left(\frac{4}{7}\right)^{-1} = \frac{7}{4} \)
3. \( \frac{9}{4} + \frac{7}{4} = \frac{16}{4} = 4 \)

б)

1. \( \left(\frac{1}{6}\right)^{-2} = 6^2 = 36 \)
2. \( 6^{-3} = \frac{1}{6^3} = \frac{1}{216} \)
3. \( 36^{-2} = \frac{1}{36^2} = \frac{1}{1296} \)
4. \( \frac{1}{216} : \frac{1}{1296} = \frac{1}{216} \cdot 1296 = 6 \)
5. \( 0,6^0 = 1 \)
6. \( 36 + 6 - 1 = 41 \)

б) (второй вариант)

1. \( 2^{-1} = \frac{1}{2} \)
2. \( 3^{-1} = \frac{1}{3} \)
3. \( \frac{1}{2} - \frac{1}{3} \cdot 6 = \frac{1}{2} - 2 = -\frac{3}{2} \)
4. \( \left(-\frac{3}{2}\right)^{-1} = -\frac{2}{3} \)

г)

1. \( 2^{-2} = \frac{1}{4} \)
2. \( 5^2 = 25 \)
3. \( 2^{-2} \cdot 5^2 = \frac{1}{4} \cdot 25 = \frac{25}{4} \)
4. \( \frac{25}{4} - 25 = \frac{25 - 100}{4} = -\frac{75}{4} \)
5. \( 10^{-2} = \frac{1}{100} \)
6. \( \frac{-\frac{75}{4}}{\frac{1}{100}} = -\frac{75}{4} \cdot 100 = -75 \cdot 25 = -1875 \)

1.162.

1. \( \left(-\frac{1}{4}\right)^{-10} = 4^{10} \)
2. \( 64^{-3} = \left(2^6\right)^{-3} = 2^{-18} \)
3. \( 0,2^4 = \left(\frac{1}{5}\right)^4 = \frac{1}{625} \)
4. \( 25^{-2} = \left(5^2\right)^{-2} = 5^{-4} = \frac{1}{625} \)
5. \( 0,125^{-1} = \left(\frac{1}{8}\right)^{-1} = 8 \)
6. \( 4^{10} \cdot 2^{-18} = \left(2^2\right)^{10} \cdot 2^{-18} = 2^{20} \cdot 2^{-18} = 2^2 = 4 \)
7. \( \frac{1}{625} \cdot \frac{1}{625} = \frac{1}{390625} \)
8. \( 4 - \frac{1}{390625} + 8 = 12 - \frac{1}{390625} = \frac{12 \cdot 390625 - 1}{390625} = \frac{4687500 - 1}{390625} = \frac{4687499}{390625} \)

Ответ: 1.159 а) 4; б) 41; б) -2/3; г) -1875. 1.162. 4687499/390625.