Страницы 13-14 номер 1.2.5, ГДЗ по алгебре за 7, 8 и 9 класс к задачнику Ткачевой
Найти значение степени: 1) \(2{,}1^0\); 2) \(\left(-5\frac{1}{2}\right)^0\); 3) \(17^{-1}\); 4) \(29^{-1}\); 5) \(\left(\frac{2}{5}\right)^{-1}\); 6) \(\left(\frac{7}{9}\right)^{-1}\); 7) \(\left(1\frac{2}{3}\right)^{-1}\); 8) \(\left(2\frac{1}{2}\right)^{-1}\); 9) \(\left(-\frac{1}{3}\right)^{-1}\); 10) \(\left(-\frac{1}{8}\right)^{-1}\); 11) \((0{,}3)^{-1}\); 12) \((0{,}7)^{-1}\); 13) \((-0{,}4)^{-1}\); 14) \((-0{,}6)^{-1}\); 15) \(\left(\frac{1}{3}\right)^{-2}\); 16) \(\left(\frac{1}{4}\right)^{-2}\); 17) \(\left(-\frac{1}{6}\right)^{-2}\); 18) \(\left(-\frac{1}{9}\right)^{-2}\); 19) \(\left(\frac{2}{3}\right)^{-2}\); 20) \(\left(\frac{3}{4}\right)^{-2}\); 21) \(\left(1\frac{1}{2}\right)^{-2}\); 22) \(\left(1\frac{1}{3}\right)^{-2}\); 23) \(\left(\frac{1}{5}\right)^{-3}\); 24) \(\left(\frac{1}{6}\right)^{-3}\); 25) \(\left(-\frac{1}{3}\right)^{-3}\); 26) \(\left(-\frac{1}{4}\right)^{-3}\); 27) \(\left(-1\frac{1}{3}\right)^{-4}\); 28) \(\left(-1\frac{1}{2}\right)^{-4}\).
1) \(2{,}1^0 = 1\);
2) \(\left(-5\frac{1}{2}\right)^0 = 1\);
3) \(17^{-1} = \frac{1}{17}\);
4) \(29^{-1} = \frac{1}{29}\);
5) \(\left(\frac{2}{5}\right)^{-1} = \frac{1}{\frac{2}{5}} = \frac{5}{2}\);
6) \(\left(\frac{7}{9}\right)^{-1} = \frac{1}{\frac{7}{9}} = \frac{9}{7}\);
7) \(\left(1\frac{2}{3}\right)^{-1} = \left(\frac{5}{3}\right)^{-1} = \frac{1}{\frac{5}{3}} = \frac{3}{5}\);
8) \(\left(2\frac{1}{2}\right)^{-1} = \left(\frac{5}{2}\right)^{-1} = \frac{1}{\frac{5}{2}} = \frac{2}{5}\);
9) \(\left(-\frac{1}{3}\right)^{-1} = \frac{1}{-\frac{1}{3}} = -3\);
10) \(\left(-\frac{1}{8}\right)^{-1} = \frac{1}{-\frac{1}{8}} = -8\);
11) \((0{,}3)^{-1} = \frac{1}{0{,}3} = \frac{1}{\frac{3}{10}} = \frac{10}{3}\);
12) \((0{,}7)^{-1} = \frac{1}{0{,}7} = \frac{1}{\frac{7}{10}} = \frac{10}{7}\);
13) \((-0{,}4)^{-1} = \frac{1}{-0{,}4} = \frac{1}{-\frac{2}{5}} = -\frac{5}{2}\);
14) \((-0{,}6)^{-1} = \frac{1}{-0{,}6} = \frac{1}{-\frac{3}{5}} = -\frac{5}{3}\);
15) \(\left(\frac{1}{3}\right)^{-2} = \frac{1}{\left(\frac{1}{3}\right)^2} = \frac{1}{\frac{1}{9}} = 9\);
16) \(\left(\frac{1}{4}\right)^{-2} = \frac{1}{\left(\frac{1}{4}\right)^2} = \frac{1}{\frac{1}{16}} = 16\);
17) \(\left(-\frac{1}{6}\right)^{-2} = \frac{1}{\left(-\frac{1}{6}\right)^2} = \frac{1}{\frac{1}{36}} = 36\);
18) \(\left(-\frac{1}{9}\right)^{-2} = \frac{1}{\left(-\frac{1}{9}\right)^2} = \frac{1}{\frac{1}{81}} = 81\);
19) \(\left(\frac{2}{3}\right)^{-2} = \frac{1}{\left(\frac{2}{3}\right)^2} = \frac{1}{\frac{4}{9}} = \frac{9}{4}\);
20) \(\left(\frac{3}{4}\right)^{-2} = \frac{1}{\left(\frac{3}{4}\right)^2} = \frac{1}{\frac{9}{16}} = \frac{16}{9}\);
21) \(\left(1\frac{1}{2}\right)^{-2} = \left(\frac{3}{2}\right)^{-2} = \frac{1}{\left(\frac{3}{2}\right)^2} = \frac{1}{\frac{9}{4}} = \frac{4}{9}\);
22) \(\left(1\frac{1}{3}\right)^{-2} = \left(\frac{4}{3}\right)^{-2} = \frac{1}{\left(\frac{4}{3}\right)^2} = \frac{1}{\frac{16}{9}} = \frac{9}{16}\);
23) \(\left(\frac{1}{5}\right)^{-3} = \frac{1}{\left(\frac{1}{5}\right)^3} = \frac{1}{\frac{1}{125}} = 125\);
24) \(\left(\frac{1}{6}\right)^{-3} = \frac{1}{\left(\frac{1}{6}\right)^3} = \frac{1}{\frac{1}{216}} = 216\);
25) \(\left(-\frac{1}{3}\right)^{-3} = \frac{1}{\left(-\frac{1}{3}\right)^3} = \frac{1}{-\frac{1}{27}} = -27\);
26) \(\left(-\frac{1}{4}\right)^{-3} = \frac{1}{\left(-\frac{1}{4}\right)^3} = \frac{1}{-\frac{1}{64}} = -64\);
27) \(\left(-1\frac{1}{3}\right)^{-4} = \left(-\frac{4}{3}\right)^{-4} = \frac{1}{\left(-\frac{4}{3}\right)^4} = \frac{1}{\frac{256}{81}} = \frac{81}{256}\);
28) \(\left(-1\frac{1}{2}\right)^{-4} = \left(-\frac{3}{2}\right)^{-4} = \frac{1}{\left(-\frac{3}{2}\right)^4} = \frac{1}{\frac{81}{16}} = \frac{16}{81}\).
Ответ: 1) \(1\); 2) \(1\); 3) \(\frac{1}{17}\); 4) \(\frac{1}{29}\); 5) \(\frac{5}{2}\); 6) \(\frac{9}{7}\); 7) \(\frac{3}{5}\); 8) \(\frac{2}{5}\); 9) \(-3\); 10) \(-8\); 11) \(\frac{10}{3}\); 12) \(\frac{10}{7}\); 13) \(-\frac{5}{2}\); 14) \(-\frac{5}{3}\); 15) \(9\); 16) \(16\); 17) \(36\); 18) \(81\); 19) \(\frac{9}{4}\); 20) \(\frac{16}{9}\); 21) \(\frac{4}{9}\); 22) \(\frac{9}{16}\); 23) \(125\); 24) \(216\); 25) \(-27\); 26) \(-64\); 27) \(\frac{81}{256}\); 28) \(\frac{16}{81}\).
Найти значение степени: 1) \(2{,}1^0\); 2) \(\left(-5\frac{1}{2}\right)^0\); 3) \(17^{-1}\); 4) \(29^{-1}\); 5) \(\left(\frac{2}{5}\right)^{-1}\); 6) \(\left(\frac{7}{9}\right)^{-1}\); 7) \(\left(1\frac{2}{3}\right)^{-1}\); 8) \(\left(2\frac{1}{2}\right)^{-1}\); 9) \(\left(-\frac{1}{3}\right)^{-1}\); 10) \(\left(-\frac{1}{8}\right)^{-1}\); 11) \((0{,}3)^{-1}\); 12) \((0{,}7)^{-1}\); 13) \((-0{,}4)^{-1}\); 14) \((-0{,}6)^{-1}\); 15) \(\left(\frac{1}{3}\right)^{-2}\); 16) \(\left(\frac{1}{4}\right)^{-2}\); 17) \(\left(-\frac{1}{6}\right)^{-2}\); 18) \(\left(-\frac{1}{9}\right)^{-2}\); 19) \(\left(\frac{2}{3}\right)^{-2}\); 20) \(\left(\frac{3}{4}\right)^{-2}\); 21) \(\left(1\frac{1}{2}\right)^{-2}\); 22) \(\left(1\frac{1}{3}\right)^{-2}\); 23) \(\left(\frac{1}{5}\right)^{-3}\); 24) \(\left(\frac{1}{6}\right)^{-3}\); 25) \(\left(-\frac{1}{3}\right)^{-3}\); 26) \(\left(-\frac{1}{4}\right)^{-3}\); 27) \(\left(-1\frac{1}{3}\right)^{-4}\); 28) \(\left(-1\frac{1}{2}\right)^{-4}\).
Степень с нулевым показателем равна единице: \(a^0 = 1\) при \(a \ne 0\). Степень с целым отрицательным показателем находится по определению: \(a^{-n} = \frac{1}{a^n}\) при натуральном \(n\) и \(a \ne 0\); единица, делённая на дробь, равна обратной дроби.
1) \(2{,}1^0 = 1\);
2) \(\left(-5\frac{1}{2}\right)^0 = 1\);
3) \(17^{-1} = \frac{1}{17}\);
4) \(29^{-1} = \frac{1}{29}\);
5) \(\left(\frac{2}{5}\right)^{-1} = \frac{1}{\frac{2}{5}} = \frac{5}{2}\);
6) \(\left(\frac{7}{9}\right)^{-1} = \frac{1}{\frac{7}{9}} = \frac{9}{7}\);
7) \(\left(1\frac{2}{3}\right)^{-1} = \left(\frac{5}{3}\right)^{-1} = \frac{1}{\frac{5}{3}} = \frac{3}{5}\);
8) \(\left(2\frac{1}{2}\right)^{-1} = \left(\frac{5}{2}\right)^{-1} = \frac{1}{\frac{5}{2}} = \frac{2}{5}\);
9) \(\left(-\frac{1}{3}\right)^{-1} = \frac{1}{-\frac{1}{3}} = -3\);
10) \(\left(-\frac{1}{8}\right)^{-1} = \frac{1}{-\frac{1}{8}} = -8\);
11) \((0{,}3)^{-1} = \frac{1}{0{,}3} = \frac{1}{\frac{3}{10}} = \frac{10}{3}\);
12) \((0{,}7)^{-1} = \frac{1}{0{,}7} = \frac{1}{\frac{7}{10}} = \frac{10}{7}\);
13) \((-0{,}4)^{-1} = \frac{1}{-0{,}4} = \frac{1}{-\frac{2}{5}} = -\frac{5}{2}\);
14) \((-0{,}6)^{-1} = \frac{1}{-0{,}6} = \frac{1}{-\frac{3}{5}} = -\frac{5}{3}\);
15) \(\left(\frac{1}{3}\right)^{-2} = \frac{1}{\left(\frac{1}{3}\right)^2} = \frac{1}{\frac{1}{9}} = 9\);
16) \(\left(\frac{1}{4}\right)^{-2} = \frac{1}{\left(\frac{1}{4}\right)^2} = \frac{1}{\frac{1}{16}} = 16\);
17) \(\left(-\frac{1}{6}\right)^{-2} = \frac{1}{\left(-\frac{1}{6}\right)^2} = \frac{1}{\frac{1}{36}} = 36\);
18) \(\left(-\frac{1}{9}\right)^{-2} = \frac{1}{\left(-\frac{1}{9}\right)^2} = \frac{1}{\frac{1}{81}} = 81\);
19) \(\left(\frac{2}{3}\right)^{-2} = \frac{1}{\left(\frac{2}{3}\right)^2} = \frac{1}{\frac{4}{9}} = \frac{9}{4}\);
20) \(\left(\frac{3}{4}\right)^{-2} = \frac{1}{\left(\frac{3}{4}\right)^2} = \frac{1}{\frac{9}{16}} = \frac{16}{9}\);
21) \(\left(1\frac{1}{2}\right)^{-2} = \left(\frac{3}{2}\right)^{-2} = \frac{1}{\left(\frac{3}{2}\right)^2} = \frac{1}{\frac{9}{4}} = \frac{4}{9}\);
22) \(\left(1\frac{1}{3}\right)^{-2} = \left(\frac{4}{3}\right)^{-2} = \frac{1}{\left(\frac{4}{3}\right)^2} = \frac{1}{\frac{16}{9}} = \frac{9}{16}\);
23) \(\left(\frac{1}{5}\right)^{-3} = \frac{1}{\left(\frac{1}{5}\right)^3} = \frac{1}{\frac{1}{125}} = 125\);
24) \(\left(\frac{1}{6}\right)^{-3} = \frac{1}{\left(\frac{1}{6}\right)^3} = \frac{1}{\frac{1}{216}} = 216\);
25) \(\left(-\frac{1}{3}\right)^{-3} = \frac{1}{\left(-\frac{1}{3}\right)^3} = \frac{1}{-\frac{1}{27}} = -27\);
26) \(\left(-\frac{1}{4}\right)^{-3} = \frac{1}{\left(-\frac{1}{4}\right)^3} = \frac{1}{-\frac{1}{64}} = -64\);
27) \(\left(-1\frac{1}{3}\right)^{-4} = \left(-\frac{4}{3}\right)^{-4} = \frac{1}{\left(-\frac{4}{3}\right)^4} = \frac{1}{\frac{256}{81}} = \frac{81}{256}\);
28) \(\left(-1\frac{1}{2}\right)^{-4} = \left(-\frac{3}{2}\right)^{-4} = \frac{1}{\left(-\frac{3}{2}\right)^4} = \frac{1}{\frac{81}{16}} = \frac{16}{81}\).
Ответ: 1) \(1\); 2) \(1\); 3) \(\frac{1}{17}\); 4) \(\frac{1}{29}\); 5) \(\frac{5}{2}\); 6) \(\frac{9}{7}\); 7) \(\frac{3}{5}\); 8) \(\frac{2}{5}\); 9) \(-3\); 10) \(-8\); 11) \(\frac{10}{3}\); 12) \(\frac{10}{7}\); 13) \(-\frac{5}{2}\); 14) \(-\frac{5}{3}\); 15) \(9\); 16) \(16\); 17) \(36\); 18) \(81\); 19) \(\frac{9}{4}\); 20) \(\frac{16}{9}\); 21) \(\frac{4}{9}\); 22) \(\frac{9}{16}\); 23) \(125\); 24) \(216\); 25) \(-27\); 26) \(-64\); 27) \(\frac{81}{256}\); 28) \(\frac{16}{81}\).
