find the product.
$-8x^5y^2 \cdot 6x^2y$

$\bigcirc$ $-8x^{10}y^2$
$\bigcirc$ $-8x^7y^3$
$\bigcirc$ $-48x^7y^3$
$\bigcirc$ $-48x^{10}y^2$

Question

find the product.
$-8x^5y^2 \cdot 6x^2y$

$\bigcirc$ $-8x^{10}y^2$
$\bigcirc$ $-8x^7y^3$
$\bigcirc$ $-48x^7y^3$
$\bigcirc$ $-48x^{10}y^2$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Product of Powers", "Simplifying Monomials" ], "new_concepts": [], "current_concepts": [ "Product of Powers", "Simplifying Monomials", "Multiplying Polynomials" ] } ## Group coefficients and like variables $$ -8x^5y^2 \cdot 6x^2y = (-8 \cdot 6) \cdot (x^5 \cdot x^2) \cdot (y^2 \cdot y^1) $$ ## Multiply coefficients and apply product of powers rule $$ \begin{aligned} -8 \cdot 6 &= -48 \ x^5 \cdot x^2 &= x^{5+2} = x^7 \ y^2 \cdot y^1 &= y^{2+1} = y^3 \end{aligned} $$ ## Combine the simplified parts $$ -48x^7y^3 $$

(A) $-8x^{10}y^2$

(B) $-8x^7y^3$

(C) $-48x^7y^3$

(D) $-48x^{10}y^2$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Simplifying Monomials" ] }

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QUESTION IMAGE

Question

Explanation:

Group coefficients and like variables

Multiply coefficients and apply product of powers rule

Combine the simplified parts

Answer: