Tính :a,7.6^10.2^20.3^6-2^19.6^19 / 9.6^19.2^9-4.3^19.2^20

Giải thích các bước giải:

$\dfrac{7.6^{10}.2^{20}.3^{6}-2^{19}.6^{19}}{9.6^{19}.2^{9}-4.3^{19}.2^{20}}$ 

$=\dfrac{7.(2.3)^{10}.2^{20}.3^{6}-2^{19}.(2.3)^{19}}{3^2.(2.3)^{19}.2^{9}-2^2.3^{19}.2^{20}}$ 

$=\dfrac{7.2^{10}.3^{10}.2^{20}.3^{6}-2^{19}.2^{19}.3^{19}}{3^2.2^{19}.3^{19}.2^{9}-2^2.3^{19}.2^{20}}$ 

$=\dfrac{7.(2^{10}.2^{20}).(3^{10}.3^{6})-(2^{19}.2^{19}).3^{19}}{(3^2.3^{19})(2^{19}.2^{9})-(2^2.2^{20}).3^{19}}$ 

$=\dfrac{7.2^{10+20}.3^{10+6}-2^{19+19}.3^{19}}{3^{2+19}.2^{19+9}-2^{2+20}.3^{19}}$ 

$=\dfrac{7.2^{30}.3^{16}-2^{38}.3^{19}}{3^{21}.2^{28}-2^{22}.3^{19}}$ 

$=\dfrac{2^{30}.3^{16}(7-2^{8}.3^{3})}{3^{19}.2^{22}(3^2.2^6-1)}$ 

$=\dfrac{2^{8}(-6905)}{3^{3}.575}$ 

$=-\dfrac{2^{8}.1381}{3^{3}.115}$