Select the correct answer to the following equation: −x3/2=−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 can first eliminate the negative signs from both sides:

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

Next, we can rewrite \(27\) as \(3^3\):

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

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

\[ \left(x^{3/2}\right)^{\frac{2}{3}} = (3^3)^{\frac{2}{3}} \]

This simplifies to:

\[ x = 3^{3 \cdot \frac{2}{3}} = 3^2 = 9 \]

Thus, the correct answer is:

9