what value of $k$ makes the equation true?

$(5a^2b^3)(6a^kb) = 30a^6b^4$

3
8
4
2

Question

what value of $k$ makes the equation true?

$(5a^2b^3)(6a^kb) = 30a^6b^4$

3
8
4
2

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", "Product Rule of Exponents" ], "new_concepts": [], "current_concepts": [ "Exponent Rules", "Product Rule of Exponents", "Polynomial Multiplication" ] } ## Simplify the left side of the equation $$ (5a^2b^3)(6a^kb) = (5 \cdot 6)(a^2 \cdot a^k)(b^3 \cdot b^1) = 30a^{2+k}b^4 $$ ## Set up the equation for the exponent of a $$ 2 + k = 6 $$ ## Solve for k $$ k = 4 $$

3

8

4

2

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Simplify the left side of the equation

Set up the equation for the exponent of a

Solve for k

Answer: