\(\left(5^2\times2^3-7^3\times2\right)\div2\times6-7\div2^5\)

\(=\left(25\times8-343\times2\right)\div2\times6-7\div32\)

\(=\left(200-686\right)\div2\times6-7\div32\)

\(=-486\div2\times6-7\div32\)

\(=-1458-0,21875\)

\(=-1458,21875\)

\(\left(5^2.2^3-7^3.2\right):\left(2.6-7:2^5\right)\\ =\left(25.8-343.2\right):\left(12-7:32\right)\\ =\left(200-686\right):\left(12-\dfrac{7}{32}\right)\\ =-486:\dfrac{377}{32}=-486.\dfrac{32}{377}=-\dfrac{15552}{377}\)

(5^2*2^3-7^3*2):2*6-7:2^5

=(25*8-343*2):3-7/32

=-162-7/32=-5191/32

a) \(\frac{75^3.3^7}{81^4.5^6}=\frac{5^3.3^3.5^3.3^7}{\left(3^4\right)^4.5^6}=\frac{5^6.3^3.3^7}{3^{16}.5^6}=\frac{3^{10}}{3^{16}}=\frac{1}{3^6}=\frac{1}{729}\)
b) \(\frac{6^6.4^2}{3^{12}.2^8}=\frac{2^6.3^6.\left(2^2\right)^2}{3^{12}.2^8}=\frac{2^6.3^6.2^4}{3^{12}.2^8}=\frac{2^{10}.3^6}{3^{12}.2^8}=\frac{2^2.1}{3^6}=\frac{4}{729}\)
c) \(\frac{34^5.2^5}{2^{14}.17^5}=\frac{2^5.17^5.2^5}{2^{14}.17^5}=\frac{2^{10}}{2^{14}}=\frac{1}{2^4}=\frac{1}{16}\)

 1/2 x 2 mũ n cộng 4 x 2 mũ n = 9 x 2 mũ n

\(a,\)\(\frac{2^5\times3^{12}\times7^8}{2^7\times3^{10}\times7^9}=\frac{3^2\times\left(2^5\times3^{10}\times7^8\right)}{2^2\times7\times\left(2^5\times3^{10}\times7^8\right)}\)\(=\frac{3^2}{2^2\times7}=\frac{9}{28}\)

\(b,\)Tương tự

:((

\(4^2\cdot120-4^3\cdot17+4^2\cdot34\)

\(=4^2\left(120-4\cdot17+34\right)\)

\(=16\left(120-68+34\right)\)

\(=16\cdot86=1088\)

\(7^3\cdot9+3^2\cdot7^4-45\cdot539\)

\(=7^3\cdot9+9\cdot7^4-45\cdot7^2\cdot11\)

\(=7^2\left(7\cdot9+9\cdot7^2-45\cdot11\right)\)

\(=49\left(63+9\cdot49-495\right)\)

\(=49\left(63+441-495\right)\)

\(=49\cdot9=441\)

\(5\cdot10^4+4\cdot10^3+6\cdot10^2+5\cdot10+9\)

\(=10\left(5\cdot10^3+4\cdot10^2+10\cdot6\right)+9\)

\(=10\left(5\cdot1000+4\cdot100+60\right)+9\)

\(=10\left(5000+400+60\right)+9\)

\(=10\cdot5460+9=54600+9=54609\)

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\(\left(9^2\cdot\dfrac{3^3}{3^7}\right)\cdot2018\)

\(=\dfrac{3^4}{3^4}\cdot2018\)

=2018