If (23 2 3 )m (34 3 4 )n = 252729 252 729 , find the values of m and n

If ($\frac{2}{3}$)m ($\frac{3}{4}$)n = $\frac{252}{729}$, find the values of m and n

Answer Details

($\frac{2}{3}$)m ($\frac{3}{4}$)n = $\frac{252}{729}$
$\frac{2^m}{4^n}$ x $\frac{3^n}{3^m}$ = 283-6
2m - 2n x 3n - m = 28 x 3-6
m - 2n = 8........(i)
-m + n = -6........(ii)
Solving the equations simultaneously
m = 4, n = -2