To solve the equation \(-x^{3/2} = -27\), we can first eliminate the negative signs on both sides:
\[ x^{3/2} = 27 \]
Next, we can raise both sides to the power of \(\frac{2}{3}\) to isolate \(x\):
\[ x = 27^{2/3} \]
Now, we can simplify \(27^{2/3}\). The cube root of 27 is 3 (since \(3^3 = 27\)), and then we square it:
\[ 27^{2/3} = (3)^2 = 9 \]
So the solution to the equation is:
\[ \boxed{9} \]