Question

i am offering 20 points for this question,answer fast....9^n+1 ×(3^-n/2)^-2 -27n) / (3^m +2)^3 =1/729 prove that m-n=2
I will surely mark you as brainliest..plz answer correctly and read the question correctly

Answer 1

Answer: please mark as brainliest

Step-by-step explanation:

Given that, ( 9^n x 3^2 x (3^-n/2)^-2 - 27^n) /( 3^3m x 2^3) = 1/27

⇒ (3^2n x 3^2 x { 3^-(-2n/2) } - 3^3n )/ 3^3m x 2^3 = 1/(3^3)

⇒ (3^2n x 3^2 x {3^n} - 3^3n )/ 3^3m x 2^3 = 3^(-3)

⇒ ( 3^3n x 3^2 - 3^3n )/ 3^3m x 2^3 = 3^(-3)

⇒ 3^3n[ 3^2 - 1] / 3^3m x 2^3 = 3^(-3)

⇒ 3^3n[ 9 - 1 ] /3^3m x 8 =  3^(-3)

⇒ 3^3n x 8 /3^3m x 8 = 3^(-3)

 ⇒ 3^(3n-3m) = 3^(-3)

comparing powers on both side, we get

3n - 3m = -3

⇒ 3(n-m) = -3

⇒ (n-m) = -1

or m-n = 1

Hence proved