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12/5.(-15/16).(-1/9)

= (-9/4).(-1/9)

=1/4

a. Ta có : 2,5 < 5,2 => 2,5³ < 5,2³

b. Ta có : 4⁵ = 1024      ;        5⁴ = 625

Vì 1024 > 625 => 4⁵ > 5⁴

\(a.2.5^3va5.2^3\)

\(2.5^3=2.125=250;5.2^3=5.8=40\)

Vì \(250>40\)

\(\Rightarrow2.5^3>5.2^3\)

\(b.4^5va5^4\)

\(4^5=1024;5^4=625\)

Vì \(1024>625\)

\(\Rightarrow4^5>5^4\)

\(c.2^8va2.5^3\)

\(2^8=256;2.5^3=2.125=250\)

Vì \(256>250\)

\(\Rightarrow2^8>2.5^3\)

2.Tìm x:

\(a.2^n+4.2^n=5.2^5\)

  \(2^n\left(1+4\right)=5.32\) 

                \(2^n.5=160\)

                    \(2^n=160:5\)

                    \(2^n=32\)

                    \(2^n=2^5\)

                \(\Rightarrow n=5\)

\(b.3^4.3^n:9=3^7\)

  \(3^4.3^n:3^2=3^7\)

        \(3^4.3^n=3^7.3^2\)

        \(3^4.3^n=3^{7+2}\)

        \(3^4.3^n=3^9\)

              \(3^n=3^9:3^4\)

              \(3^n=3^{9-4}\)

              \(3^n=3^5\)

          \(\Rightarrow n=5\)

\(c.6.2^n+3.2^n=9.2^n\)

     \(2^n\left(6+3\right)=9.2^n\)

                   \(2^n.9=9.2^n\)

                  \(\Rightarrow2^n=9:9\)

                  \(\Rightarrow2^n=1\)

                  \(\Rightarrow2^n=2^0\)

                    \(\Rightarrow n=0\)

Chúc bạn học tốt!

a) \(2^2\cdot5^2-64:2^3\)

\(=4\cdot25-2^6:2^3\)

\(=100-2^3=100-8\)

\(=92\)

b) \(3^5\cdot9:243\)

\(=3^5\cdot9:3^5=9\)

c) \(4\cdot2^5\cdot2^3\cdot\dfrac{1}{16}\)

\(=2^{10}\cdot\dfrac{1}{2^4}=2^6\)

\(=64\)

d) \(\dfrac{11\cdot3^{22}\cdot3^7-9^{15}}{3^{28}}\)

\(=\dfrac{11\cdot3^{29}-\left(3^2\right)^{15}}{3^{28}}\)

\(=\dfrac{11\cdot3^{29}-3^{30}}{3^{28}}=\dfrac{3^{29}\left(11-3\right)}{3^{28}}\)

\(=\dfrac{3^{29}\cdot8}{3^{28}}=3\cdot8=24\)

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