which expression is equivalent to $(4y^2)^3(3y^2)$?

* $12y^8$
* $12y^{12}$
* $192y^8$
* $192y^{12}$

Question

which expression is equivalent to $(4y^2)^3(3y^2)$?

* $12y^8$
* $12y^{12}$
* $192y^8$
* $192y^{12}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Exponent Rules", "Algebraic Simplification", "Power of a Product Rule" ], "new_concepts": [], "current_concepts": [ "Exponent Rules", "Algebraic Simplification", "Power of a Product Rule" ] } ## Apply power of a product rule $$ (4y^2)^3 = 4^3 \cdot (y^2)^3 = 64y^6 $$ ## Multiply the simplified terms $$ (64y^6)(3y^2) = (64 \cdot 3)(y^6 \cdot y^2) $$ ## Simplify coefficients and exponents $$ 192y^{6+2} = 192y^8 $$

(A) $12y^8$

(B) $12y^{12}$

(C) $192y^8$

(D) $192y^{12}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Exponent Rules" ] }

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QUESTION IMAGE

Question

Explanation:

Apply power of a product rule

Multiply the simplified terms

Simplify coefficients and exponents

Answer: