The problem has a nicer answer if it is actually

x^(3/2) = 27

You solve this by raising both sides to the 2/3 power

(x^(3/2))^(2/3) = 27^(2/3)

x^((2/3)*(2/3)) = ((27^(1/3))^2

x = 3^2

x = 9

You can also solve it using logarithms.

(3/2)Log[x] = Log[27]

Log[x] = (2/3)Log[27] ≈ (2/3)*1.43136 ≈ .95424

x = 9

If your original problem is the one you want, then the answer is found by multiplying by 2 and taking the cube root.

X^3/2 = 27

x^3 = 27*2

x = 27^(1/3)*2^(1/3)

x = 3*2^(1/3) ≈ 3*1.25992 ≈ 3.77976

x^(3/2) = 27

You solve this by raising both sides to the 2/3 power

(x^(3/2))^(2/3) = 27^(2/3)

x^((2/3)*(2/3)) = ((27^(1/3))^2

x = 3^2

x = 9

You can also solve it using logarithms.

(3/2)Log[x] = Log[27]

Log[x] = (2/3)Log[27] ≈ (2/3)*1.43136 ≈ .95424

x = 9

If your original problem is the one you want, then the answer is found by multiplying by 2 and taking the cube root.

X^3/2 = 27

x^3 = 27*2

x = 27^(1/3)*2^(1/3)

x = 3*2^(1/3) ≈ 3*1.25992 ≈ 3.77976