\(32^{-x}.16^x=2048\)
\(\Leftrightarrow (2^5)^{-x}.(2^4)^{-x}=2048\)
\(\Leftrightarrow 2^{-5x}.2^{4x}=2^{11} \)
\(\Leftrightarrow 2^{-5x+4x}=2^{11} \)
\(\Leftrightarrow 2^{-x}=2^{11} \)
\(\Rightarrow x = -11 \)
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