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

Question

Responses

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

9
9

−3
negative 3

−9

Answer 1

To solve the equation \( -x^{3/2} = -27 \), we can simplify it as follows:

1. Multiply both sides by -1: \[ x^{3/2} = 27 \]

2. To eliminate the exponent, raise both sides to the power of \( \frac{2}{3} \): \[ x = 27^{2/3} \]

3. Calculate \( 27^{2/3} \):

   • First, find \( 27^{1/3} \), which is \( 3 \) (since \( 3^3 = 27 \)).
   • Then square it: \[ 3^2 = 9 \]

So, \( x = 9 \).

Therefore, the correct answer is: 9.