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

(10^{-3} \cdot 10 \cdot 10^{k} = 10^{-3} = \frac{1}{10^{3}})

-3
-1
0
1

Question

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

(10^{-3} \cdot 10 \cdot 10^{k} = 10^{-3} = \frac{1}{10^{3}})

-3
-1
0
1

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [], "current_concepts": [ "Exponent Rules", "Negative Exponents" ] } ## Simplify the left side of the equation $$ \begin{aligned} 10^{-3} \cdot 10 \cdot 10^k &= 10^{-3} \cdot 10^1 \cdot 10^k \ &= 10^{-3 + 1 + k} \ &= 10^{k - 2} \end{aligned} $$ ## Set up the equation with the right side $$ \begin{aligned} 10^{k - 2} &= 10^{-3} \ k - 2 &= -3 \end{aligned} $$ ## Solve for k $$ \begin{aligned} k &= -3 + 2 \ k &= -1 \end{aligned} $$

(A) -3

(B) -1

(C) 0

(D) 1

{ "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

Set up the equation with the right side

Solve for k

Answer: