{"@context":"https://schema.org/","@type":"Quiz","name":"

Which expression is equivalent to $\\left(m^{4}q^{4}z^{-1}\\right)\\left(mq^{5}z^{3}\\right)$, where $m$, $q$, and $z$ are positive?

","hasPart":{"@type":"Question","typicalAgeRange":"12-22","educationalAlignment":[{"@type":"AlignmentObject","alignmentType":"educationalSubject","targetName":"SAT"},{"@type":"AlignmentObject","alignmentType":"educationalLevel","targetName":"SAT","educationalFramework":"Common Core","targetUrl":"https://classnotes.xyz/mcqs/sat-math-advanced-math-multiple-choice-question-220"}],"about":{"@type":"Thing","name":"Math, Advanced Math, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Advanced Math","Duplicate"],"name":"

Which expression is equivalent to $\\left(m^{4}q^{4}z^{-1}\\right)\\left(mq^{5}z^{3}\\right)$, where $m$, $q$, and $z$ are positive?

","comment":{"@type":"Comment","text":"

Choice B is correct. Applying the commutative property of multiplication, the expression $\\left(m^{4}q^{4}z^{-1}\\right)\\left(mq^{5}z^{3}\\right)$ can be rewritten as $\\left(m^{4}m\\right)\\left(q^{4}q^{5}\\right)\\left(z^{-1}z^{3}\\right)$. For positive values of $x,\\left(x^{a}\\right)\\left(x^{b}\\right)=x^{a+b}$. Therefore, the expression $\\left(m^{4}m\\right)\\left(q^{4}q^{5}\\right)\\left(z^{-1}z^{3}\\right)$ can be rewritten as $\\left(m^{4+1}\\right)\\left(q^{4+5}\\right)\\left(z^{-1+3}\\right)$, or $m^{5}q^{9}z^{2}$.

Choice A is incorrect and may result from multiplying, not adding, the exponents.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

"},"encodingFormat":"text/markdown","text":"

Which expression is equivalent to $\\left(m^{4}q^{4}z^{-1}\\right)\\left(mq^{5}z^{3}\\right)$, where $m$, $q$, and $z$ are positive?

","suggestedAnswer":[{"@type":"Answer","position":0,"encodingFormat":"text/html","text":"

$m^{4}q^{20}z^{-3}$

"},{"@type":"Answer","position":2,"encodingFormat":"text/html","text":"

$m^{6}q^{8}z^{-1}$

"},{"@type":"Answer","position":3,"encodingFormat":"text/html","text":"

$m^{20}q^{12}z^{-2}$

"}],"acceptedAnswer":{"@type":"Answer","position":1,"encodingFormat":"text/html","text":"

$m^{5}q^{9}z^{2}$

","comment":{"@type":"Comment","text":"

Choice D is incorrect and may result from conceptual or calculation errors.

"},"answerExplanation":{"@type":"Comment","text":"

Choice D is incorrect and may result from conceptual or calculation errors.

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-advanced-math-multiple-choice-question-220"}

Which expression is equivalent to $\left(m^{4}q^{4}z^{-1}\right)\left(mq^{5}z^{3}\right)$, where $m$, $q$, and $z$ are positive?