which are perfect cubes? check all that apply.

64
$x^{16}$
$8x^3$
$27x^4$
$81x^6$
$125x^9$

Question

which are perfect cubes? check all that apply.

64
  $x^{16}$
  $8x^3$
  $27x^4$
  $81x^6$
  $125x^9$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Perfect Cubes" ], "new_concepts": [], "current_concepts": [ "Perfect Cubes" ] } ## Analyze numerical coefficients and variable exponents $$ \begin{aligned} &\text{A term } a x^n \text{ is a perfect cube if } a = b^3 \text{ for some integer } b, \text{ and } n = 3k \text{ for some integer } k \ge 0. \end{aligned} $$ ## Evaluate each option $$ \begin{aligned} &64 = 4^3 \quad (\text{Perfect cube})\ &x^{16} \implies 16 \text{ is not divisible by } 3 \quad (\text{Not a perfect cube})\ &8x^3 = (2x)^3 \quad (\text{Perfect cube})\ &27x^4 \implies 4 \text{ is not divisible by } 3 \quad (\text{Not a perfect cube})\ &81x^6 \implies 81 = 3^4 \text{ is not a perfect cube} \quad (\text{Not a perfect cube})\ &125x^9 = (5x^3)^3 \quad (\text{Perfect cube}) \end{aligned} $$ ## Identify correct choices $$ \text{The perfect cubes are: } 64, \ 8x^3, \text{ and } 125x^9. $$

64

$x^{16}$

$8x^3$

$27x^4$

$81x^6$

$125x^9$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Perfect Cubes" ] }

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QUESTION IMAGE

Question

Explanation:

Analyze numerical coefficients and variable exponents

Evaluate each option

Identify correct choices

Answer: