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\(=\frac{3^7\cdot\left(2^4\right)^3}{\left(2^2\cdot3\right)^5\cdot\left(3^3\right)^2}\)
\(=\frac{3^7\cdot2^{12}}{2^{10}\cdot3^5\cdot3^6}\)
\(=\frac{3^7\cdot2^{12}}{2^{10}\cdot3^{11}}\)
\(=\frac{2^2}{3^4}\)
\(=\frac{4}{81}\)
\(\frac{3^7.16^3}{12^5.27^2}=\frac{3^7.\left(2^4\right)^3}{\left(2^2.3\right)^5.\left(3^3\right)^2}=\frac{3^7.2^{12}}{2^{10}.3^5.3^6}=\frac{3^7.2^{12}}{2^{10}.3^{11}}=\frac{2^2}{3^4}=\frac{4}{81}\)
\(\dfrac{3}{5}.\dfrac{6}{7}+\dfrac{3}{7}:\dfrac{5}{3}-\dfrac{2}{7}:1\dfrac{2}{3}.\)
\(=\dfrac{3}{5}.\dfrac{6}{7}+\dfrac{3}{7}.\dfrac{3}{5}-\dfrac{2}{7}.\dfrac{3}{5}.\)
\(=\dfrac{3}{5}\left(\dfrac{6}{7}+\dfrac{3}{7}-\dfrac{2}{7}\right).\)
\(=\dfrac{3}{5}.1=\dfrac{3}{5}.\)
Vậy.....
\(\dfrac{3^7.16^3}{12^5.27^2}=\dfrac{3^7.\left(2^4\right)^3}{\left(2^2.3\right)^5.\left(3^3\right)^2}.\)
\(=\dfrac{3^7.2^{12}}{\left(2^2\right)^5.3^5.3^6}=\dfrac{3^7.2^{12}}{2^{10}.3^{11}}.\)
\(=\dfrac{2^2}{3^4}=\dfrac{4}{81}.\)
Vậy.....
\(\frac{2^{19}\cdot27^4}{6^7\cdot16^3}\)
\(=\frac{2^{19}\cdot3^{12}}{2^7\cdot3^7\cdot2^{12}}\)
\(=\frac{2^{19}\cdot3^{12}}{2^{19}\cdot3^7}\)
\(=3^5\)
\(=243\)
\(\frac{2^{19}.27^4}{6^7.16^3}\)
\(=\frac{2^{19}.\left(3^3\right)^4}{2^7.3^7.\left(2^4\right)^3}\)
\(=\frac{2^{19}.3^{12}}{2^7.3^7.2^{12}}\)
=\(3^5=243\)
3^7. 16^3=3^7. (2^4)^3 =3^7.2^12 =3^2.2^2=2^2 =4
12^5.21^3=(3.2^2)^5.(7.3)^3=3^5.2^10.7^3.3^3=7^3.3^3=343.3=1029