Select the correct answer to the following equation: −x exponent3/2=−27

Question

.(1 point)
Responses

−9
negative 9

−3
negative 3

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

9

Answer 1

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

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

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

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

Calculate \(27^{\frac{1}{3}}\) first, which is \(3\), since \(3^3 = 27\). Then we square it:

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

Thus, we find:

\[ x = 9 \]

So the correct answer is:

9