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: Option D
Explanation
((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