Thực hiện phép tính:
a. \(\frac{2}{3}:\frac{{ - 6}}{9} + \frac{1}{7}\);
b. \(\frac{{ - 3}}{{11}} \cdot \frac{5}{9} + \frac{4}{9} \cdot \frac{{ - 3}}{{11}}\);
c. \(\frac{{{9^5}{{.8}^2}}}{{{{27}^3}.16}}\)
Dựa vào quy tắc tính với số hữu tỉ, lũy thừa.
a. \(\frac{2}{3}:\frac{{ - 6}}{9} + \frac{1}{7}\)\( = \frac{2}{3}.\frac{{ - 9}}{6} + \frac{1}{7}\)\( = - 1 + \frac{1}{7}\)\( = \frac{{ - 6}}{7}\).
b. \(\frac{{ - 3}}{{11}} \cdot \frac{5}{9} + \frac{4}{9} \cdot \frac{{ - 3}}{{11}}\)\( = \frac{{ - 3}}{{11}} \cdot \left( {\frac{5}{9} + \frac{4}{9}} \right)\)\( = \frac{{ - 3}}{{11}}.1\)\( = \frac{{ - 3}}{{11}}\).
c. \(\frac{{{9^5}{{.8}^2}}}{{{{27}^3}.16}}\)\( = \frac{{{{\left( {{3^2}} \right)}^5}.{{\left( {{2^3}} \right)}^2}}}{{{{\left( {{3^3}} \right)}^3}{{.2}^4}}}\)\( = \frac{{{3^{10}}{{.2}^6}}}{{{3^9}{{.2}^4}}}\)\( = {3.2^2} = 3.4 = 12\).
