Select the correct answer to the following equation: −x^3/2=−27.(1 point)

To solve the equation \(-x^{3/2} = -27\), we can first simplify it by multiplying both sides by -1:

\[ x^{3/2} = 27 \]

Next, to solve for \(x\), we can raise both sides to the power of \(\frac{2}{3}\):

\[ x = 27^{\frac{2}{3}} \]

Calculating \(27^{\frac{1}{3}}\):

\[ 27^{\frac{1}{3}} = 3 \]

Now we can square this result:

\[ 27^{\frac{2}{3}} = (27^{\frac{1}{3}})^2 = 3^2 = 9 \]

Therefore, the solution is:

\[ x = 9 \]

So, the correct answer is \( \boxed{9} \).