\(m=\dfrac{2^7\cdot3^5+2^4\cdot3^9}{2^6\cdot3^5+2^3\cdot3^9}\)

\(m=\dfrac{2^4\cdot3^5\cdot\left(2^3+3^4\right)}{2^3\cdot3^5\cdot\left(2^3+3^4\right)}\)

\(m=\dfrac{2^4\cdot3^5}{2^3\cdot3^5}\)

\(m=\dfrac{2^4}{2^3}\)

\(m=2^{4-3}\)

\(m=2\)

f) \(\frac{25^2.20^4}{5^{10}.4^5}=\frac{\left(5^2\right)^5.\left(4.5\right)^4}{5^{10}.4^5}=\frac{5^{10}.5^4.4^4}{5^{10}.4^5}=\frac{5^{14}.4^4}{5^{10}.4^5}=\frac{5^4}{4}\)

i) \(\frac{9^{15}.81^4}{27^8.3^{20}}=\frac{\left(3^2\right)^{15}.\left(3^4\right)^4}{\left(3^3\right)^8.3^{20}}=\frac{3^{30}.3^{16}}{3^{24}.3^{20}}=\frac{3^{46}}{3^{44}}=3^2=9\)

f) Ta có: \(\frac{25^2.20^4}{5^{10}.4^5}\)= \(\frac{\left(5^2\right)^2.\left(4.5\right)^4}{5^{10}.4^5}\)= \(\frac{5^4.4^4.5^4}{5^{10}.4^5}\)= \(\frac{5^8.4^4}{5^{10}.4^5}\)= \(\frac{1}{5^2.4}\)=\(\frac{1}{100}\).

i) Ta có: \(\frac{9^{15}.81^4}{27^8.3^{20}}\)= \(\frac{\left(3^2\right)^{15}.\left(3^4\right)^4}{\left(3^3\right)^8.3^{20}}\)= \(\frac{3^{30}.3^8}{3^{24}.3^{20}}\)= \(\frac{3^{38}}{3^{44}}\)=\(\frac{1}{3^6}\)= \(\frac{1}{729}\)

\(\frac{2^{15}.2+3}{8^6.3^9}=\frac{2^{16}+3}{2^{18}.3.3^8}=\frac{2^{16}+3}{2^{16}.2^2.3.3^8}=\frac{1}{2^2.3^8}\)

b)\(\frac{1}{6}\)

c)\(\frac{3}{16}\)

e)243

a)\(\frac{36^7}{2^{15}\cdot27^5}=\frac{36^7}{\left(2^3\right)^5\cdot27^5}\)

\(=\frac{36^7}{\left(8\cdot27\right)^5}=\frac{36^7}{216^5}\)

\(=\frac{36^7}{36^5\cdot6^5}=\frac{36^5\cdot36^2}{36^5\cdot6^5}\)

\(=\frac{36^2}{6^5}=\frac{\left(6^2\right)^2}{6^5}=\frac{6^4}{6^5}=\frac{1}{6}\)

\(\)

\(\frac{2^7\cdot3^6}{6^5\cdot8^2}=\frac{2^7\cdot3^6}{6^5\cdot\left(2^3\right)^2}=\frac{2\cdot3^6}{6^5}\)

\(=\frac{2\cdot3^6}{\left(3\cdot2\right)^5}=\frac{2\cdot3^6}{3^5\cdot2^5}\)

\(=\frac{3}{2^4}=\frac{3}{16}\)

\(M=\frac{\left(3^2\right)^4.\left(3^3\right)^5.3^6.3^4}{3^8.\left(3^4\right)^4.3^5.\left(2^3\right)^2}=\frac{3^8.3^{15}.3^6.3^4}{3^8.3^{16}.3^5.2^6}=\frac{3^{29}.3^4}{3^{29}.2^6}=\frac{1.81}{1.64}=\frac{81}{64}\)

A=663552 

   (22⋅3)6⋅84⋅35

A=   663552 

  4096⋅177147⋅4096

A=   663552
   2972033482752
A=    1
4478976

\(M=\frac{9^4.27^5.3^6.3^4}{3^8.81^4.243.8^2}\)

\(M=\frac{\left(3^2\right)^4.\left(3^3\right)^5.3^6.3^4}{3^8.\left(3^4\right)^4.\left(3^5\right).\left(2^3\right)}\)

\(M=\frac{3^8.3^{15}.3^6.3^4}{3^8.3^{16}.3^5.8}\)

\(M=\frac{3^{33}}{3^{29}.8}\)

\(M=\frac{3^4}{1.8}\)

\(M=\frac{81}{8}\)

Chúc bạn học tốt !!! 

Sửa hộ mk : 

\(8^2=2^9\)

Kết quả : \(\frac{81}{512}\)

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