what value of $n$ makes the equation true?

$(2x^9y^n)(4x^2y^{10}) = 8x^{11}y^{20}$

1
30
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Question

what value of $n$ makes the equation true?

$(2x^9y^n)(4x^2y^{10}) = 8x^{11}y^{20}$

1
30
10
2

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Polynomial Multiplication" ], "new_concepts": [ "Exponent Rules", "Product Rule of Exponents" ], "current_concepts": [ "Polynomial Multiplication", "Exponent Rules", "Product Rule of Exponents" ] } ## Simplify the left side of the equation $$ (2x^9y^n)(4x^2y^{10}) = (2 \cdot 4)(x^9 \cdot x^2)(y^n \cdot y^{10}) = 8x^{11}y^{n+10} $$ ## Equate the exponents of y $$ y^{n+10} = y^{20} \implies n + 10 = 20 $$ ## Solve for n $$ n = 10 $$

1

30

10

2

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

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QUESTION IMAGE

Question

Explanation:

Simplify the left side of the equation

Equate the exponents of y

Solve for n

Answer: