Question

${9}^{n} \times {3}^{2} \times {3}^{n} - {27}^{n} \div ( {3}^{m} \times 2) ^{3} = {3}^{ - 3}$
show that m-n = 1

pls solve quick​

Answer 1

Answer:

Hello.  I hope this is helpful...

I think there's a mistake in the statement of the problem.  I am presuming that m and n are to be integers.

Multiplying through by 2³ and 3³ (and using 9 = 3² and 27 = 3³), the equation becomes

$2^3\times3^{3n+5} - 3^{3(n-m+1)} = 2^3$

If 3n+5 ≥ 0, then the first and third terms are even integers, so the middle must be an even integer, too.  But this is not possible.

If 3n+5 < 0, multiply through by 3^{-3n-5} and a similar contradiction is reached.

Answer 2

Hope it helps ! mark as brainliest