If \((\frac{2}{3})^{m} (\frac{3}{4})^{n} = \frac{256}{729}\), find the values of m and n.
A. m = 4, n = 2 B. m = -4, n = -2 C. m = -4, n =2 D. m = 4, n = -2 E. m = -2, n = 4 Correct Answer: DExplanation(\(\frac{2}{3}\))m (\(\frac{3}{4}\))n = \(\frac{256}{729}\) \(\frac{2^m}{4^n}\) x \(\frac{3^n}{3^m}\) = \(\frac{2^{8}}{3^{6}}\) \(2^{m} \div 2^{2n} = 2^{8}; 3^{n} \div 3^{m} = 3^{-6}\) m - 2n = 8........(i) -m + n = -6........(ii) Solving the equations simultaneously m = 4, n = -2 |