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Which choices are real numbers? Check all that apply.

A. [tex](-531441)^{1 / 12}[/tex]
B. [tex](-131072)^{1 / 16}[/tex]
C. [tex](-5776)^{1 / 7}[/tex]
D. [tex](-256)^{1 / 11}[/tex]



Answer :

GinnyAnswer
To determine which of the given choices are real numbers, we need to examine each expression and see if the result yields a real number.

### Choice A: [tex]\((-531441)^{1 / 12}\)[/tex]
To find [tex]\((-531441)^{1 / 12}\)[/tex]:
[tex]\[ (-531441)^{1 / 12} \approx -3.0 \][/tex]
Since [tex]\(-3.0\)[/tex] is a real number, Choice A is a real number.

### Choice B: [tex]\((-131072)^{1 / 16}\)[/tex]
To find [tex]\((-131072)^{1 / 16}\)[/tex]:
[tex]\[ (-131072)^{1 / 16} \approx -2.0885475648548275 \][/tex]
Since [tex]\(-2.0885475648548275\)[/tex] is a real number, Choice B is a real number.

### Choice C: [tex]\((-5776)^{1 / 7}\)[/tex]
To find [tex]\((-5776)^{1 / 7}\)[/tex]:
[tex]\[ (-5776)^{1 / 7} \approx -3.4464764246261175 \][/tex]
Since [tex]\(-3.4464764246261175\)[/tex] is a real number, Choice C is a real number.

### Choice D: [tex]\((-256)^{1 / 11}\)[/tex]
To find [tex]\((-256)^{1 / 11}\)[/tex]:
[tex]\[ (-256)^{1 / 11} \approx -1.6555065597696215 \][/tex]
Since [tex]\(-1.6555065597696215\)[/tex] is a real number, Choice D is a real number.

Therefore, all four choices, A, B, C, and D, are real numbers.

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