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

Question

Responses

−3
negative 3

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

9
9

−9

Answer 1

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

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

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

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

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

1. Find the cube root of 27, which is 3.
2. Then square that result: \( 3^2 = 9 \).

Thus, \( x = 9 \).

Therefore, the correct answer is:

9