Select the correct answer to the following equation: −x32=−27

Question

.(1 point)
Responses

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

9
9

−9
negative 9

−3

Answer 1

To solve the equation \(-x^{32} = -27\), we first divide both sides by -1:

\[ x^{32} = 27 \]

Next, we take the 32nd root of both sides:

\[ x = 27^{1/32} \]

Since \(27\) can be expressed as \(3^3\), we have:

\[ x = (3^3)^{1/32} = 3^{3/32} \]

This gives us a positive solution for \(x\). Thus, the solution to the equation is positive, and the possible answers provided include negative answers, which leads us to conclude that the only viable response is:

no solution, the answer cannot be negative.