which equation is equivalent to $16^{2p} = 32^{p+3}$?

$8^{4p} = 8^{4p+3}$
$8^{4p} = 8^{4p+12}$
$2^{8p} = 2^{5p+15}$
$2^{8p} = 2^{5p+3}$

Question

which equation is equivalent to $16^{2p} = 32^{p+3}$?

$8^{4p} = 8^{4p+3}$
$8^{4p} = 8^{4p+12}$
$2^{8p} = 2^{5p+15}$
$2^{8p} = 2^{5p+3}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Exponential Equations" ], "new_concepts": [], "current_concepts": [ "Exponential Equations", "Properties of Exponents" ] } ## Express bases with a common base of 2 $$ \begin{aligned} 16 &= 2^4 \ 32 &= 2^5 \end{aligned} $$ ## Substitute and apply exponent rules $$ \begin{aligned} (2^4)^{2p} &= (2^5)^{p+3} \ 2^{4 \cdot 2p} &= 2^{5(p+3)} \ 2^{8p} &= 2^{5p+15} \end{aligned} $$

(A) $8^{4p} = 8^{4p+3}$

(B) $8^{4p} = 8^{4p+12}$

(C) $2^{8p} = 2^{5p+15}$

(D) $2^{8p} = 2^{5p+3}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Exponential Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Express bases with a common base of 2

Substitute and apply exponent rules

Answer: