what is the cube root of $-1,000p^{12}q^3$?

* $-10p^4$
* $-10p^4q$
* $10p^4$
* $10p^4q$

Question

what is the cube root of $-1,000p^{12}q^3$?

* $-10p^4$
* $-10p^4q$
* $10p^4$
* $10p^4q$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Cube Roots", "Exponent Rules", "Radical Simplification" ], "current_concepts": [ "Cube Roots", "Exponent Rules", "Radical Simplification" ] } ## Express the cube root mathematically $$ \sqrt[3]{-1,000p^{12}q^3} $$ ## Apply the product rule for radicals $$ \sqrt[3]{-1,000} \cdot \sqrt[3]{p^{12}} \cdot \sqrt[3]{q^3} $$ ## Simplify each component $$ \begin{aligned} \sqrt[3]{-1,000} &= -10 \ \sqrt[3]{p^{12}} &= p^{12/3} = p^4 \ \sqrt[3]{q^3} &= q^{3/3} = q^1 = q \ \sqrt[3]{-1,000p^{12}q^3} &= -10p^4q \end{aligned} $$

(A) $-10p^4$

(B) $-10p^4q$

(C) $10p^4$

(D) $10p^4q$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Radical Simplification" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Express the cube root mathematically

Apply the product rule for radicals

Simplify each component

Answer: