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9 tháng 9 2016

\(\frac{2^7.9^3}{6^5.8^2}=\frac{2^7.\left(3^2\right)^3}{\left(2.3\right)^5.\left(2^3\right)^2}=\frac{2^7..3^6}{2^5.3^5.2^6}=\frac{2^7.3^6}{2^{11}.3^5}=\frac{3}{2^4}=\frac{3}{16}\)

18 tháng 9 2016

a) \(\frac{2^7}{6^5}\times\frac{9^3}{8^8}=\frac{2^7}{2^5\times3^5}\times\frac{3^6}{2^{24}}=\frac{2^7\times3^6}{2^{29}\times3^5}=\frac{3}{4194304}\)

b) \(\frac{6^3+3\times6^2+3^3}{-13}=\frac{2^3\times3^3+3\times2^2\times3^2+3^3}{-13}=\frac{3^3\left(2^3+2^2+1\right)}{-13}=\frac{27\times13}{-13}=-27\)

17 tháng 11 2021

\(\dfrac{2^7\cdot9^3}{6^5\cdot8^2}=\dfrac{2^7\cdot3^6}{3^5\cdot2^5\cdot2^6}=\dfrac{3}{2^3}=\dfrac{3}{8}\)

30 tháng 11 2016

a/\(\frac{4^5.9^4-2.6^9}{2^{10}.3^8+6^8.20}=\frac{\left(2^2\right)^5.\left(3^2\right)^4-2.\left(2.3\right)^9}{2^{10}.3^8+\left(2.3\right)^8.2^2.5}\)

= \(\frac{2^{10}.3^8-2.2^9.3^9}{2^{10}.3^8+2^8.3^8.2^2.5}=\frac{2^{10}.3^8-2^{10}.3^9}{2^{10}.3^8+2^{10}.3^8.5}=\frac{2^{10}.3^8.\left(1-3\right)}{2^{10}.3^8\left(1+5\right)}=\frac{1-3}{1+5}=\frac{-2}{6}=-3\)

 

1:

a: \(A=2+3\sqrt{x^2+1}>=3\cdot1+2=5\)

Dấu = xảy ra khi x=0

b: \(B=\sqrt{x+8}-7>=-7\)

Dấu = xảy ra khi x=-8

17 tháng 7 2016

\(a\)\(\left(4^2.4^3\right):2^{10}\)

   \(=4^5:2^{10}\)

   \(=\left(2^2\right)^5:2^{10}\)

   \(=2^{10}:2^{10}\)

   \(=1\)  

    \(b\)\(\left(0,6\right)^5:\left(0,2\right)^6\)

    \(=\left(\frac{3}{5}\right)^5:\left(\frac{1}{5}\right)^6\)

     \(=\frac{3^5}{5^5}:\frac{1^6}{5^6}\)

      \(=\frac{3^5}{5^5}.5^6\)

        \(=\frac{3^5.5^6}{5^5}\)

        \(=3^5.5\)

         \(=243.5\)

          \(=1215\)

 \(c\)\(\left(2^7.9^3\right):\left(6^5.8^2\right)\)

     \(=\left[2^7.\left(3^2\right)^3\right]:\left[\left(2.3\right)^5.\left(2^4\right)^2\right]\)

      \(=\left(2^7.3^6\right):\left[2^5.3^5.2^8\right]\)

       \(=\left(2^7.3^6\right).\left(\frac{1}{2^5.3^5.2^8}\right)\)

         \(=\frac{2^7.3^6.1}{\left(2^5.2^8\right).3^5}\)

           \(=\frac{2^7.3^6}{2^{13}.3^5}\)

           \(=\frac{3}{2^6}\)

           \(=\frac{3}{64}\)