Tính một cách hợp lí

a) $\frac{- 5}{7} \times \frac{2}{11} + \frac{- 5}{7} \times \frac{9}{11} + \frac{5}{7}$

= $\frac{- 5}{7} \times (\frac{2}{11} + \frac{9}{11}) + \frac{5}{7}$ = $\frac{- 5}{7} \times 1 + \frac{5}{7} = \frac{- 5}{7} + \frac{5}{7} = 0.$

b) $[(\frac{- 3}{8} + \frac{11}{23}) / \frac{5}{9} + (\frac{- 5}{8} + \frac{12}{23}) / \frac{5}{9}] \times \frac{- 11}{325}$

= $[(\frac{- 3}{8} + \frac{11}{23} + \frac{- 5}{8} + \frac{12}{23}) / \frac{5}{9}] \times \frac{- 11}{325}$

= $[(\frac{- 3}{8} + \frac{- 5}{8}) + (\frac{11}{23} + \frac{12}{23})] / \frac{5}{9} \times \frac{- 11}{325}$

= $[(- 1) + 1] / \frac{5}{9} \times \frac{- 11}{325} = (0 / \frac{5}{9}) \times \frac{- 11}{325} = 0 \times \frac{- 11}{325} = 0.$

c*) Nhận xét: Với hai số hữu tỉ x, y ta có:

$(x \times y)^{n} = x^{n} \times y^{n}; (\frac{x}{y})^{n} = \frac{x^{n}}{y^{n}} (y \neq 0);$

$\frac{15^{5}}{5^{5}} - (- 0.25)^{2} \times 4^{2}$

= $(\frac{15}{5})^{5} - (- 0.25 \times 4)^{2} = 3^{5} - (- 1)^{2} = 243 - 1 = 242.$

d*) $- \frac{2^{15} \times 9^{4}}{6^{6} \times 8^{3}} + 0.75 \times \frac{- 1}{2} + 0.375 .$

= $- \frac{2^{15} \times (3^{2})^{4}}{(2 \times 3)^{6} \times (2^{3})^{3}} + (- 0.375) + 0.375 .$

= $- \frac{2^{15} \times 3^{8}}{2^{6} \times 3^{6} \times 2^{9}} + [(- 0.375) + 0.375]$

= $- \frac{2^{15} \times 3^{8}}{2^{15} \times 3^{6}} + 0 = - 3^{2} = - 9.$