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
jamb 1983mathematics

The correct answer is D. m = 4, n = -2

(\(\frac{2}{3}\))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

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