a)\(32^{-n}\cdot16^n=2048\)

\(\left(2^5\right)^{-n}\cdot\left(2^4\right)^n\)=2048

\(2^{-5n}\cdot2^{4n}\)=\(2^{11}\)

\(2^{-5n+4n}=2^{11}\)

\(2^{-x}=2^{11}\)

\(\Rightarrow x=-11\)

b)\(2^{-1}\cdot2^n+4\cdot2^n=9\cdot2^5\)

\(\frac{1}{2}\cdot2^n+4\cdot2^n=288\)

\(2^n\left(\frac{1}{2}+4\right)=288\)

\(2^n\cdot\frac{9}{2}=288\)

\(2^n=288:\frac{9}{2}\)

\(2^n=64\)

\(2^n=2^6\)

\(\Rightarrow n=6\)

a) 32^-n . 16ⁿ = 2048

\(\frac{1}{32n}\) . 16ⁿ = 2048

\(\frac{1}{2^n.16^n}\) . 16ⁿ = 2048

\(\frac{1}{2^n}\) = 2048

2^-n = 2048

2^-n = 2¹¹

\(\Rightarrow\) -n = 11

\(\Rightarrow\) n = -11

Vậy n = -11

2^-1.2ⁿ+4.2ⁿ=9.2⁵

=>2^n-1+2².2ⁿ=9.2⁵

=>2^n-1+2ⁿ⁺²=9.2⁵

=>2^n-1.(2³+1)=9.2⁵

=>2^n-1.9=9.2⁵

=>2^n-1=2⁵

=>n-1=5=>n=6

Ta có: \(2^{-1}\cdot2^n+4\cdot2^n=9\cdot2^5\)

\(\Leftrightarrow2^n\cdot2^{-1}+2^n\cdot2^2=9\cdot2^5\)

\(\Leftrightarrow2^n\cdot\left(2^{-1}+2^2\right)=9\cdot2^5\)

\(\Leftrightarrow2^n\cdot\dfrac{9}{2}=9\cdot2^5\)

\(\Leftrightarrow2^n=9\cdot2^5:\dfrac{9}{2}=2^5\cdot9\cdot\dfrac{2}{9}=2^6\)

hay n=6

Vậy: n=6

\(\frac{1}{2}.2^n+4.2^n=9.2^5\)

\(2^n.\left(\frac{1}{2}.4\right)=288\)

\(2^n.2=288\)

\(2^n=288:2\)

\(2^n=144\)

       Suy ra n ko tìm được

Ta có : 

\(\frac{1}{2}\cdot2^n+4\cdot2^n=\frac{9}{2}\cdot2^5\)

\(=>\left(\frac{1}{2}+4\right)\cdot2^n=9\cdot2^5\)

\(=>\left(\frac{1}{2}+\frac{8}{2}\right)\cdot2^n=9\cdot2^5\)

\(=>\frac{9}{2}\cdot2^n=\frac{9}{2}\cdot2^5\)

\(=>2^n=2^5\)

\(=>n=5\)

\(\frac{1}{2}\times2^n+4\times2^n=9\times2^5\)

\(2^n\times\left(\frac{1}{2}+4\right)=9\times2^5\)

\(2^n\times\left(\frac{1+8}{4}\right)=9\times2^5\)

\(2^n\times\frac{9}{2^2}=9\times2^5\)

\(\frac{2^n}{2^2}=2^5\)

\(2^n=2^5\times2^2\)

\(2^n=2^7\)

\(n=7\)

\(\dfrac{1}{2}\cdot2^n+4\cdot2^n=9\cdot2^5\\ \Rightarrow2^n\left(\dfrac{1}{2}+4\right)=9\cdot2^5\\ \Rightarrow2^n\cdot\dfrac{9}{2}=9\cdot2^5\\ \Rightarrow2^{n-1}\cdot9=9\cdot2^5\\ \Rightarrow n-1=5\\ \Rightarrow n=6\)

Giúp mk với

2ⁿ.(1/2+4)=9.32

2ⁿ*4,5=288

2ⁿ=64=2⁶

=> n=6

\(2^{-1}.2^n+4.2^n=9.2^5\)

\(2^n.2=9.2^5\)

\(\Rightarrow2^n=9.2^4\)

Ko có n nhé bn

a) \(\frac{1}{9}.27^n=3^n\)

\(=>\frac{27^n}{9}=3^n\)

\(=>3^n=3^n=>n=1\)

b) \(2^{-1}.2^n+4.2^n=9.2^5\)

\(=>2^{n-1}.2^2.2^n=9.2^5\)

\(=>2^{n-1}.2^{2+n}=9.2^5\)

\(=>2^{2n+1}=9.5^2\)

\(=>n=\)

Câu b đề sai hay sao ấy số xấu lắm