3 times the square root of 27 is equal to 3 to the power of 'n', what is 'n'

3√27 = 3ⁿ

3√(9*3) = 3ⁿ

9√3 = 3ⁿ      write the left side in terms of exponents using the base of 3

(3)² * 3^1/2 = 3ⁿ

(3)^5/2 = 3ⁿ

So n = 5/2

3*√27 = 3*√3³ = √(3²*3³) = √(3⁵) = 3^5/2

So n = 5/2

how does 3 squared times 3 to the power of 1/2 =3 5/2