Question
Select the correct answer to the following equation: −x32=−27
.(1 point)
Responses
9
9
no solution, the answer cannot be negative
no solution, the answer cannot be negative
−3
negative 3
−9
.(1 point)
Responses
9
9
no solution, the answer cannot be negative
no solution, the answer cannot be negative
−3
negative 3
−9
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To solve the equation \( -x^{32} = -27 \), we can first eliminate the negative signs from both sides:
\[ x^{32} = 27 \]
Next, we need to solve for \( x \) by taking the 32nd root of both sides:
\[ x = 27^{1/32} \]
Since \( 27 = 3^3 \), we can rewrite it:
\[ x = (3^3)^{1/32} = 3^{3/32} \]
This means \( x \) is a positive number because any even root of a positive number is also positive.
Thus, the equation has one valid solution, and while none of the provided responses are the 32nd root of 27, it confirms there is **no solution, the answer cannot be negative** is incorrect because we have a positive solution.
Therefore, out of the given options, the closest and most relevant responses would be:
**no solution, the answer cannot be negative** - is still technically incorrect.
None of the provided answers are exactly correct since \( x \) is a positive value around \( 1.5 \) but since we are tasked to select among the incorrect provided options, I'd say:
**no solution, the answer cannot be negative** (though this is misleading given there is a solution, but no options match the actual solution).
\[ x^{32} = 27 \]
Next, we need to solve for \( x \) by taking the 32nd root of both sides:
\[ x = 27^{1/32} \]
Since \( 27 = 3^3 \), we can rewrite it:
\[ x = (3^3)^{1/32} = 3^{3/32} \]
This means \( x \) is a positive number because any even root of a positive number is also positive.
Thus, the equation has one valid solution, and while none of the provided responses are the 32nd root of 27, it confirms there is **no solution, the answer cannot be negative** is incorrect because we have a positive solution.
Therefore, out of the given options, the closest and most relevant responses would be:
**no solution, the answer cannot be negative** - is still technically incorrect.
None of the provided answers are exactly correct since \( x \) is a positive value around \( 1.5 \) but since we are tasked to select among the incorrect provided options, I'd say:
**no solution, the answer cannot be negative** (though this is misleading given there is a solution, but no options match the actual solution).
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