47. Найдите значения выражений: a) 33\(\cdot\)\(\left\)\(\frac{1}{11}\right\)^2-5\(\frac{5}{11}\) б) 13\(\frac{5}{17}\)+51\(\cdot\)\(\left\)\(\frac{1}{17}\right\)^2 в) 81\(\cdot\)\(\left\)\(\frac{1}{9}\right\)^3-14\(\frac{2}{9}\) г) 11\(\frac{3}{7}\)+98\(\cdot\)\(\left\)\(\right\)

Решение:

а) \(33\cdot\left(\frac{1}{11}\right)^2-5\frac{5}{11} = 33\cdot\frac{1}{121}-5\frac{5}{11} = \frac{33}{121} - \frac{60}{11} = \frac{3}{11} - \frac{60}{11} = \frac{3-60}{11} = \frac{-57}{11} = -5\frac{2}{11}\)

б) \(13\frac{5}{17}+51\cdot\left(\frac{1}{17}\right)^2 = 13\frac{5}{17}+51\cdot\frac{1}{289} = \frac{226}{17} + \frac{51}{289} = \frac{226}{17} + \frac{3}{17} = \frac{226+3}{17} = \frac{229}{17} = 13\frac{8}{17}\)

в) \(81\cdot\left(\frac{1}{9}\right)^3-14\frac{2}{9} = 81\cdot\frac{1}{729} - 14\frac{2}{9} = \frac{81}{729} - \frac{128}{9} = \frac{1}{9} - \frac{128}{9} = \frac{1-128}{9} = \frac{-127}{9} = -14\frac{1}{9}\)

г) \(11\frac{3}{7}+98\cdot\left(\right)\) - неполное условие.

Ответ:

• а) \(-5\frac{2}{11}\)
• б) \(13\frac{8}{17}\)
• в) \(-14\frac{1}{9}\)
• г) Условие неполное.