Question

8. Find the value of m :( 2/9)^3 X ( 2/9)^−6 = ( 4/81)^2m−1​

Answer 1

$( \frac{2}{9})^{3} \times ( \frac{2}{9} )^{ - 6} = (\frac{4}{81})^{2m - 1} \\ \\ { (\frac{2}{9} )}^{3 + ( - 6)} = [{( \frac{2}{9} )}^{2} ]^{2m - 1} \\ \\ (\frac{2}{9})^{3 - 6} = ( \frac{2}{9})^{4m - 2} \\ \\ ( \frac{2}{9})^{ - 3} = (\frac{2}{9}) ^{4m - 2} \\ \\ here \: the \: \frac{5}{9}(base) gets \: cancelled \\ by \: comparing \: both \: sides \\ \\ - 3 = 4m - 2 \\ - 3 + 2 = 4m \\ - 1 = 4m \\m = \frac{ - 1}{4} = - 0.25$