what is the value of (b) in the equation below?

\\frac{5^6}{5^2} = a^b\

* 3
* 4
* 5
* 8

Question

what is the value of (b) in the equation below?

\\frac{5^6}{5^2} = a^b\

* 3
* 4
* 5
* 8

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" ], "new_concepts": [], "current_concepts": [ "Exponent Rules", "Quotient Rule for Exponents" ] } ## Apply the quotient rule for exponents $$ \frac{5^6}{5^2} = 5^{6-2} = 5^4 $$ ## Equate to the given expression and solve for b $$ 5^4 = a^b \implies a = 5, \quad b = 4 $$

(A) 3

(B) 4

(C) 5

(D) 8

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Apply the quotient rule for exponents

Equate to the given expression and solve for b

Answer: