[2ⁿ+¹ (3ⁿ)]² / 36ⁿ = 9ⁿ+² / 2ⁿ

2²ⁿ+² x 3²ⁿ / (4 x 9)ⁿ = 9ⁿ+² / 2ⁿ

2²ⁿ+² x 9ⁿ / (2² x 9)ⁿ = 9ⁿ+² / 2ⁿ

2²ⁿ+² x 9ⁿ / (2²ⁿ x 9ⁿ) = 9ⁿ+² / 2ⁿ

2²ⁿ+²-²ⁿ = 9ⁿ+² / 2ⁿ

2² = 9ⁿ+² / 2ⁿ

2² x 2ⁿ = 9ⁿ+²

2ⁿ+² = 9ⁿ+²

Only possibility for n+2 = 0 for this equation to be satisfied (i.e 2^0 = 9^0 = 1)

n + 2 = 0
n = -2

Alternatively,

2ⁿ+² = 9ⁿ+²

Take ln on both sides,

ln 2ⁿ+² = ln 9ⁿ+²

(n+2)ln2 = (n+2)ln9

(n+2)(ln 2 - ln9) = 0

n + 2 = 0 since (ln2 - ln9) is negative

n = -2

Just swap n for x accordingly. Only the n superscript is available on my keyboard so it was used as a substitute.

Tks!