Asked by cloudicus
Select the correct answer to the following equation: −x3/2=−27
.(1 point)
Responses
−3
negative 3
−9
negative 9
9
9
no solution, the answer cannot be negative
.(1 point)
Responses
−3
negative 3
−9
negative 9
9
9
no solution, the answer cannot be negative
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To solve the equation \(-x^{3/2} = -27\), we can first eliminate the negative signs from both sides:
\[ x^{3/2} = 27 \]
Next, we can rewrite \(27\) as \(3^3\):
\[ x^{3/2} = 3^3 \]
To solve for \(x\), we can raise both sides to the power of \(\frac{2}{3}\):
\[
\left(x^{3/2}\right)^{\frac{2}{3}} = (3^3)^{\frac{2}{3}}
\]
This simplifies to:
\[
x = 3^{3 \cdot \frac{2}{3}} = 3^2 = 9
\]
Thus, the correct answer is:
**9**
\[ x^{3/2} = 27 \]
Next, we can rewrite \(27\) as \(3^3\):
\[ x^{3/2} = 3^3 \]
To solve for \(x\), we can raise both sides to the power of \(\frac{2}{3}\):
\[
\left(x^{3/2}\right)^{\frac{2}{3}} = (3^3)^{\frac{2}{3}}
\]
This simplifies to:
\[
x = 3^{3 \cdot \frac{2}{3}} = 3^2 = 9
\]
Thus, the correct answer is:
**9**
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