what is the value of y in the product of powers below?

(8^{3} \cdot 8^{-5} \cdot 8^{y} = 8^{-2} = \frac{1}{8^{2}})

Question

what is the value of y in the product of powers below?

(8^{3} \cdot 8^{-5} \cdot 8^{y} = 8^{-2} = \frac{1}{8^{2}})

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Exponent Rules" ], "new_concepts": [], "current_concepts": [ "Exponent Rules", "Negative Exponents" ] } ## Simplify the product of powers using exponent rules $$ \begin{aligned} 8^3 \cdot 8^{-5} \cdot 8^y &= 8^{-2} \ 8^{3 + (-5) + y} &= 8^{-2} \ 8^{-2 + y} &= 8^{-2} \end{aligned} $$ ## Equate the exponents to solve for y $$ \begin{aligned} -2 + y &= -2 \ y &= 0 \end{aligned} $$ What is the value of y in the product of powers below? $8^3 \cdot 8^{-5} \cdot 8^y = 8^{-2} = \frac{1}{8^2}$ 0 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Exponent Rules" ] }

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QUESTION IMAGE

Question

Explanation:

Simplify the product of powers using exponent rules

Equate the exponents to solve for y

Answer: