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

Question

Responses

9
9

−9
negative 9

−3
negative 3

no solution, the answer cannot be negative

Answer 1

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

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

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

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

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

1. Calculate \( 27^{1/3} \), which is the cube root of 27. The cube root of 27 is 3.
2. Then, raise that result to the power of 2: \( 3^2 = 9 \).

So,

\[ x = 9 \]

Therefore, the correct answer is:

9