vào đây nha https://coccoc.com/search/math#query=+3%5E%E2%88%921%C2%B73%5En%2B6%C2%B73%5En%E2%88%921%3D7%C2%B736++

\(3^{-1}\cdot3^n+6\cdot3^{n-1}=7\cdot3^6\)

\(3^{n-1}+6\cdot3^{n-1}=7\cdot3^6\)

\(3^{n-1}\left(1+6\right)=7\cdot3^6\)

\(3^{n-1}\cdot7=7\cdot3^6\)

\(\Rightarrow3^{n-1}=3^6\)

\(\Rightarrow n-1=6\)

\(n=6+1=7\)

\(3^{-1}.3^n+6.3^{n-1}=7.3^6\)

\(\Leftrightarrow\)\(3^{n-1}.6=7.3^6\)

Tới đây bạn tự giải đi nhé.

P/s: Thi thì bạn phải tự giải nhé, bài dễ như vậy mà bạn cũng lười động não thì đắp mềm ngủ cho rồi

a: \(5^3\cdot25^n=5^{3n}\)

\(\Leftrightarrow5^{3n}=5^3\cdot5^{2n}\)

=>3n=2n+3

hay n=3

b: \(a^{\left(2n+6\right)\left(3n-9\right)}=1\)

=>(2n+6)(3n-9)=0

=>n=-3 hoặc n=3

c: \(\dfrac{1}{3}\cdot3^n=7\cdot3^2\cdot3^4-2\cdot3^n\)

\(\Leftrightarrow3^n\cdot\dfrac{1}{3}+3^n\cdot2=7\cdot3^6\)

\(\Leftrightarrow3^n=3^7\)

hay n=7

=\(\frac{2^5.3^6\left(3-1\right)}{2^5.3^6}=2\)

\(\frac{2^5.3^7-2^5.3^6}{2^5.3^6}=\frac{2^5.\left(3^7-3^6\right)}{2^5.3^6}=\frac{2^5.1458}{2^5.729}=\frac{1458}{729}=2\)

Vậy mới chuẩn nè:

\(\frac{2^5.3^7-2^5.3^6}{2^5.3^6}=\frac{2^5.3^6\left(3^1-1\right)}{2^5.3^6}=3-1=2\)

Bạn dùng t/c phân phối với rút gọn là được

2:

\(B=3^{n+2}-2^{n+2}+3^n-2^n\)

\(=3^n\cdot9+3^n-2^n\cdot4-2^n\)

\(=3^n\cdot10-2^n\cdot5\)

\(=3^n\cdot10-2^{n-1}\cdot10⋮10\)

\(\frac{2^{12}.3^5-\left(2^2\right)^6.3^6}{2^{12}.\left(3^2\right)^3+\left(2^3\right)^4.3^3}\)

\(\frac{2^{12}.3^5.\left(1-3^{ }\right)}{2^{12}.3^3.\left(3^3-1\right)}\)

\(\frac{2^{12}.3^5.\left(-2\right)}{2^{12}.3^3.8}\)

\(\frac{3^2.\left(-1\right)}{4}\)

\(\frac{-9}{4}\)

VẬy.......................

nhớ tk cho mình nha

\(\frac{5.\left(2^2.3^2\right)^9.\left(2^2\right)^6-2.\left(2^2.3\right)^{14}.3^4}{5.2^{28}.3^{18}+7.2^{29}.3^{18}}\)

\(=\frac{5.2^{18}.3^{18}.2^{12}-2.2^{28}.3^{14}.3^4}{2^{28}.3^{18}.\left(5+7.2\right)}\)

\(=\frac{5.2^{30}.3^{18}-2^{29}.3^{18}}{2^{28}.3^{18}.19}=\frac{2^{28}.3^{18}.\left(5.4-2\right)}{2^{28}.3^{18}.19}\)

\(=\frac{5.4-2}{19}=\frac{18}{19}\)

\(a)A=\dfrac{2^{12}.3^5-4^6.9^2}{\left(2^2.3\right)^6+8^4.3^5}-\dfrac{5^{10}.7^3-25^5.49^2}{\left(125.7\right)^3+5^9.14^3}\)

\(A=\dfrac{2^{12}.3^5-\left(2^2\right)^63.\left(3^2\right)^2}{\left(2^2\right)^6.3^6+\left(2^3\right)^4.3^5}-\dfrac{5^{10}.7^3-\left(5^2\right)^5.\left(7^2\right)^2}{\left(5^3\right)^3.7^3+5^9.\left(7.2\right)^3}\)

\(A=\dfrac{2^{12}.3^5-2^{12}.3^5}{2^{12}.3^6+2^{12}.3^5}-\dfrac{5^{10}.7^3-5^{10}.7^4}{5^6.7^3+5^9.7^3.2^3}\)

\(A=\dfrac{0}{2^{12}.3^6+2^{12}.3^5}-\dfrac{5^{10}.7^3\left(1-7\right)}{5^6.7^3\left(1+5^3+2^3\right)}\)

\(A=0-\dfrac{5^4.\left(-6\right)}{1+125+8}\)

\(A=0-\dfrac{625.\left(-6\right)}{134}\)

\(A=\dfrac{-3750}{134}\)\(=\dfrac{-1875}{67}\)

\(b)3^{n+2}-2^{n+2}+3^n-2^n\)

\(=3^n.3^2-2^n.2^2+3^n-2^n\)

\(=(3^n.9+3^n)-\left(2^n.4+2^n\right)\)

\(=3^n.10-2^n.5\)

\(=3^n.10-2^{n-1}.10\)

\(=10\left(3^n-2^{n-1}\right)⋮10\)

\(Suy\) \(ra:\) \(3^{n+2}-2^{n+2}+3^n-2^n⋮10\)

b. Ta có: \(3^{n +2}-2^{n+2}+3^n-2^n\)

\(=\left(3^{n+2}+3^n\right)-\left(2^{n+2}+2^n\right)\)

\(=\left(3^n.3^2+3^n\right)-\left(2^{n-1}.2^3+2^{n-1}.2\right)\)

\(=3^n.\left(3^2+1\right)-2^{n-1}\left(2^3+2\right)\)

\(=3^n.10-2^{n-1}.10⋮10\)