which expressions are equivalent to $2^5 \cdot 2^4$? check all that apply.

$2^9$
$2^{20}$
$2 \cdot 2^8$
$2^{10} \cdot 2^2$
$2^{-2} \cdot 2^{11}$
$(2 \cdot 2 \cdot 2 \cdot 2 \cdot 2)(2 \cdot 2 \cdot 2 \cdot 2)$

Question

which expressions are equivalent to $2^5 \cdot 2^4$? check all that apply.

$2^9$
  $2^{20}$
  $2 \cdot 2^8$
  $2^{10} \cdot 2^2$
  $2^{-2} \cdot 2^{11}$
  $(2 \cdot 2 \cdot 2 \cdot 2 \cdot 2)(2 \cdot 2 \cdot 2 \cdot 2)$

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" ], "new_concepts": [], "current_concepts": [ "Exponent Rules" ] } ## Simplify the given expression $$ 2^5 \cdot 2^4 = 2^{5+4} = 2^9 $$ ## Evaluate each option $$ \begin{aligned} &\text{Option 1: } 2^9 \quad (\text{Equivalent}) \ &\text{Option 2: } 2^{20} \quad (\text{Not equivalent}) \ &\text{Option 3: } 2 \cdot 2^8 = 2^1 \cdot 2^8 = 2^{1+8} = 2^9 \quad (\text{Equivalent}) \ &\text{Option 4: } 2^{10} \cdot 2^2 = 2^{12} \quad (\text{Not equivalent}) \ &\text{Option 5: } 2^{-2} \cdot 2^{11} = 2^{-2+11} = 2^9 \quad (\text{Equivalent}) \ &\text{Option 6: } (2 \cdot 2 \cdot 2 \cdot 2 \cdot 2)(2 \cdot 2 \cdot 2 \cdot 2) = 2^5 \cdot 2^4 = 2^9 \quad (\text{Equivalent}) \end{aligned} $$

(A) $2^9$

(B) $2^{20}$

(C) $2 \cdot 2^8$

(D) $2^{10} \cdot 2^2$

(E) $2^{-2} \cdot 2^{11}$

(F) $(2 \cdot 2 \cdot 2 \cdot 2 \cdot 2)(2 \cdot 2 \cdot 2 \cdot 2)$

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Simplify the given expression

Evaluate each option

Answer: