Theo đề ta có : \(32^{-n}.16^n=2048\)
\(\Rightarrow\frac{1}{32^n}.16^n=2048\)
\(\Rightarrow\frac{16^n}{32^n}=2048\)
\(\Rightarrow\left(\frac{16}{32}\right)^n=\left(\frac{1}{2}\right)^n=2048\)
\(\Rightarrow\frac{1}{2^n}=2048\)
\(\Rightarrow2^n=\frac{1}{2048}\)
\(\Rightarrow2^n=\frac{1}{2^{11}}\Rightarrow1=2^n.2^{11}\)
\(\Rightarrow2^n=2^{-11}\Rightarrow n=-11\) ( bởi vì tích của 2 số nghịch đảo bao giờ cũng bằng 1)
qui ước \(x^{-a}=\frac{1}{x^a}\)
ta có
\(32^{-n}.16^n=2048\Rightarrow\frac{1}{32^n}.16^n=2^{10}\Rightarrow\frac{16^n}{32^n}=2^{10}\)
\(\Rightarrow\left(\frac{16}{32}\right)^n=\frac{1}{2^n}=2^{10}\Rightarrow2^{-n}=2^{10}\Rightarrow-n=10\Rightarrow n=-10\)
