Ta có:

a) $\frac{−5}{7} . \frac{2}{11} + \frac{−5}{7} . \frac{9}{11}+\frac{5}{7}$;

=$\frac{−5}{7} . (\frac{2}{11} + \frac{9}{11})+\frac{5}{7}$; 

=$\frac{-5}{7} + \frac{5}{7}= 0$

b) $[(\frac{−3}{8}+\frac{11}{23}): \frac{5}{9} + (\frac{−5}{8}+\frac{12}{23}):\frac{5}{9}].\frac{−11}{325}$;

=$[(\frac{−3}{8}+\frac{11}{23} + \frac{−5}{8}+\frac{12}{23}):\frac{5}{9}] . \frac{−11}{325}$;

=$(-1+1) : \frac{5}{9}] . \frac{−11}{325}$

=$0.  \frac{−11}{325} = 0$

c*)

Với hai số hữu tỉ x, y ta có:

$(x.y)^{n}=x^{n}.y^{n}$;

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

 Vậy $ 15^{5}5^{5}−(−0,25)^{2} . 4^{2}$;

=$(\frac{15}{5})^{5}−(−0,25.4)^{2}$

$=3^{5}−(−1)^{2}$

$=242$

d*)$−\frac{2^{15} . 9^{4}}{6^{6} . 8^{3}}+0,75 . \frac{−1}{2}+0,375$.

=$−\frac{2^{15} . (3^{2})^{4}}{(2 . 3)^{6} . (2^{3})^{3}}+ (-0,375)+0,375$.

= $\frac{−2^{15}.3^{8}}{2^{6}.3^{6}.2^{9}}$

=$−\frac{2^{15} . 3^{8}}{2^{15} . 3^{6}}$

= $-3^{2}=-9$