已知：\(12^m = 18\),求\(2^{\frac{2m-1}{m-2}}\)的值。
\(12^m = 18\)
\(3^m \cdot 2^{2m} = 18\)
\(3^m \cdot 2^{2m-1} = \frac{18}{2} \)
\(3^m \cdot 2^{2m-1} = 9\)
\(3^m \cdot 2^{2m-1} = 3^2\)
\(3^{m-2} \cdot 2^{2m-1} = 1\)
\((3^{m-2} \cdot 2^{2m-1})^{\frac{1}{m-2}} = 1^{\frac{1}{m-2}}\)
\(3^{\frac{m-2}{m-2}} \cdot 2^{\frac{2m-1}{m-2}} = 1 \)
\(3 \cdot 2^{\frac{2m-1}{m-2}} =1 \)
\(2^{\frac{2m-1}{m-2}} = \frac{1}{3} \)