Select the correct answer to the following equation: −x3/2=−27 .(1 point) Responses no solution, the answer cannot be negative no solution, the answer cannot be negative −9 negative 9 −3 negative 3 9

Answer 1

To solve the equation \( -x^{3/2} = -27 \), we start by removing the negative sign from both sides:

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

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

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

First, we will find \( 27^{\frac{1}{3}} \):

\[ 27^{\frac{1}{3}} = 3 \quad (\text{since } 3^3 = 27) \]

Now we square that result:

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

Thus, the solution is:

\[ x = 9 \]

So the correct answer is:

9.