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

Question

Responses

−9
negative 9

9
9

no solution, the answer cannot be negative
no solution, the answer cannot be negative

−3

Answer 1

To solve the equation \( -x^{3/2} = -27 \), we can first remove the negative signs from both sides:

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

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

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

We can simplify \( 27^{\frac{2}{3}} \). First, we find the cube root of 27:

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

Now we square this result:

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

So, \( x = 9 \).

Thus, the correct answer is:

9