To solve the equation \( -x^{3/2} = -27 \), we can first eliminate the negative signs from both sides:
\[ x^{3/2} = 27 \]
Next, we raise both sides to the power of \( \frac{2}{3} \) to solve for \( x \):
\[ x = 27^{\frac{2}{3}} \]
Calculating \( 27^{\frac{1}{3}} \) gives us 3 (since \( 3^3 = 27 \)). Therefore,
\[ 27^{\frac{2}{3}} = (27^{\frac{1}{3}})^2 = 3^2 = 9 \]
So, the solution is:
\[ x = 9 \]
The correct answer is:
9