Страница 12 номер 1.2.1, ГДЗ по алгебре за 7, 8 и 9 класс к задачнику Ткачевой
Вычислить: 1) \(30^2\); 2) \(0{,}3^2\); 3) \(\left(\frac{2}{5}\right)^2\); 4) \(\left(\frac{11}{13}\right)^2\); 5) \((-0{,}1)^2\); 6) \(\left(-\frac{5}{8}\right)^2\); 7) \(\left(1\frac{2}{3}\right)^2\); 8) \(\left(2\frac{1}{2}\right)^2\); 9) \(0{,}1^3\); 10) \(0{,}3^3\); 11) \(\left(\frac{2}{3}\right)^3\); 12) \(\left(\frac{4}{5}\right)^3\); 13) \((-0{,}2)^3\); 14) \((-0{,}5)^3\); 15) \(\left(1\frac{1}{2}\right)^3\); 16) \(\left(1\frac{1}{3}\right)^3\).
1) \(30^2 = 30 \cdot 30 = 900\);
2) \(0{,}3^2 = 0{,}3 \cdot 0{,}3 = 0{,}09\);
3) \(\left(\frac{2}{5}\right)^2 = \frac{2}{5} \cdot \frac{2}{5} = \frac{4}{25}\);
4) \(\left(\frac{11}{13}\right)^2 = \frac{11}{13} \cdot \frac{11}{13} = \frac{121}{169}\);
5) \((-0{,}1)^2 = (-0{,}1) \cdot (-0{,}1) = 0{,}01\);
6) \(\left(-\frac{5}{8}\right)^2 = \left(-\frac{5}{8}\right) \cdot \left(-\frac{5}{8}\right) = \frac{25}{64}\);
7) \(\left(1\frac{2}{3}\right)^2 = \left(\frac{5}{3}\right)^2 = \frac{5}{3} \cdot \frac{5}{3} = \frac{25}{9} = 2\frac{7}{9}\);
8) \(\left(2\frac{1}{2}\right)^2 = \left(\frac{5}{2}\right)^2 = \frac{5}{2} \cdot \frac{5}{2} = \frac{25}{4} = 6\frac{1}{4}\);
9) \(0{,}1^3 = 0{,}1 \cdot 0{,}1 \cdot 0{,}1 = 0{,}001\);
10) \(0{,}3^3 = 0{,}3 \cdot 0{,}3 \cdot 0{,}3 = 0{,}027\);
11) \(\left(\frac{2}{3}\right)^3 = \frac{2}{3} \cdot \frac{2}{3} \cdot \frac{2}{3} = \frac{8}{27}\);
12) \(\left(\frac{4}{5}\right)^3 = \frac{4}{5} \cdot \frac{4}{5} \cdot \frac{4}{5} = \frac{64}{125}\);
13) \((-0{,}2)^3 = (-0{,}2) \cdot (-0{,}2) \cdot (-0{,}2) = -0{,}008\);
14) \((-0{,}5)^3 = (-0{,}5) \cdot (-0{,}5) \cdot (-0{,}5) = -0{,}125\);
15) \(\left(1\frac{1}{2}\right)^3 = \left(\frac{3}{2}\right)^3 = \frac{3}{2} \cdot \frac{3}{2} \cdot \frac{3}{2} = \frac{27}{8} = 3\frac{3}{8}\);
16) \(\left(1\frac{1}{3}\right)^3 = \left(\frac{4}{3}\right)^3 = \frac{4}{3} \cdot \frac{4}{3} \cdot \frac{4}{3} = \frac{64}{27} = 2\frac{10}{27}\).
Ответ: 1) \(900\); 2) \(0{,}09\); 3) \(\frac{4}{25}\); 4) \(\frac{121}{169}\); 5) \(0{,}01\); 6) \(\frac{25}{64}\); 7) \(2\frac{7}{9}\); 8) \(6\frac{1}{4}\); 9) \(0{,}001\); 10) \(0{,}027\); 11) \(\frac{8}{27}\); 12) \(\frac{64}{125}\); 13) \(-0{,}008\); 14) \(-0{,}125\); 15) \(3\frac{3}{8}\); 16) \(2\frac{10}{27}\).
Вычислить: 1) \(30^2\); 2) \(0{,}3^2\); 3) \(\left(\frac{2}{5}\right)^2\); 4) \(\left(\frac{11}{13}\right)^2\); 5) \((-0{,}1)^2\); 6) \(\left(-\frac{5}{8}\right)^2\); 7) \(\left(1\frac{2}{3}\right)^2\); 8) \(\left(2\frac{1}{2}\right)^2\); 9) \(0{,}1^3\); 10) \(0{,}3^3\); 11) \(\left(\frac{2}{3}\right)^3\); 12) \(\left(\frac{4}{5}\right)^3\); 13) \((-0{,}2)^3\); 14) \((-0{,}5)^3\); 15) \(\left(1\frac{1}{2}\right)^3\); 16) \(\left(1\frac{1}{3}\right)^3\).
Степень с натуральным показателем — это произведение одинаковых множителей: \(a^2 = a \cdot a\), \(a^3 = a \cdot a \cdot a\). Смешанное число перед возведением в степень записываем неправильной дробью.
1) \(30^2 = 30 \cdot 30 = 900\);
2) \(0{,}3^2 = 0{,}3 \cdot 0{,}3 = 0{,}09\);
3) \(\left(\frac{2}{5}\right)^2 = \frac{2}{5} \cdot \frac{2}{5} = \frac{4}{25}\);
4) \(\left(\frac{11}{13}\right)^2 = \frac{11}{13} \cdot \frac{11}{13} = \frac{121}{169}\);
5) \((-0{,}1)^2 = (-0{,}1) \cdot (-0{,}1) = 0{,}01\);
6) \(\left(-\frac{5}{8}\right)^2 = \left(-\frac{5}{8}\right) \cdot \left(-\frac{5}{8}\right) = \frac{25}{64}\);
7) \(\left(1\frac{2}{3}\right)^2 = \left(\frac{5}{3}\right)^2 = \frac{5}{3} \cdot \frac{5}{3} = \frac{25}{9} = 2\frac{7}{9}\);
8) \(\left(2\frac{1}{2}\right)^2 = \left(\frac{5}{2}\right)^2 = \frac{5}{2} \cdot \frac{5}{2} = \frac{25}{4} = 6\frac{1}{4}\);
9) \(0{,}1^3 = 0{,}1 \cdot 0{,}1 \cdot 0{,}1 = 0{,}001\);
10) \(0{,}3^3 = 0{,}3 \cdot 0{,}3 \cdot 0{,}3 = 0{,}027\);
11) \(\left(\frac{2}{3}\right)^3 = \frac{2}{3} \cdot \frac{2}{3} \cdot \frac{2}{3} = \frac{8}{27}\);
12) \(\left(\frac{4}{5}\right)^3 = \frac{4}{5} \cdot \frac{4}{5} \cdot \frac{4}{5} = \frac{64}{125}\);
13) \((-0{,}2)^3 = (-0{,}2) \cdot (-0{,}2) \cdot (-0{,}2) = -0{,}008\);
14) \((-0{,}5)^3 = (-0{,}5) \cdot (-0{,}5) \cdot (-0{,}5) = -0{,}125\);
15) \(\left(1\frac{1}{2}\right)^3 = \left(\frac{3}{2}\right)^3 = \frac{3}{2} \cdot \frac{3}{2} \cdot \frac{3}{2} = \frac{27}{8} = 3\frac{3}{8}\);
16) \(\left(1\frac{1}{3}\right)^3 = \left(\frac{4}{3}\right)^3 = \frac{4}{3} \cdot \frac{4}{3} \cdot \frac{4}{3} = \frac{64}{27} = 2\frac{10}{27}\).
Ответ: 1) \(900\); 2) \(0{,}09\); 3) \(\frac{4}{25}\); 4) \(\frac{121}{169}\); 5) \(0{,}01\); 6) \(\frac{25}{64}\); 7) \(2\frac{7}{9}\); 8) \(6\frac{1}{4}\); 9) \(0{,}001\); 10) \(0{,}027\); 11) \(\frac{8}{27}\); 12) \(\frac{64}{125}\); 13) \(-0{,}008\); 14) \(-0{,}125\); 15) \(3\frac{3}{8}\); 16) \(2\frac{10}{27}\).
