Select the correct answer to the following equation: −x^3/2=−27

Question

.(1 point)
Responses

−3
negative 3

−9
negative 9

9
9

no solution, the answer cannot be negative

Answer 1

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

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

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

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

Calculating \(27^{2/3}\):

1. \(27 = 3^3\), so: \[ 27^{2/3} = (3^3)^{2/3} \] \[ = 3^{3 \cdot (2/3)} = 3^2 = 9 \]

Therefore, the solution is:

\[ x = 9 \]

Thus, the correct answer is:

9