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

Which expression represents the product of $\\left(x^{-6}y^{3}z^{5}\\right)$ and $\\left(x^{4}z^{5}+y^{8}z^{-7}\\right)$?

","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-160"}],"about":{"@type":"Thing","name":"Math, Advanced Math, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Advanced Math","Duplicate"],"name":"

Which expression represents the product of $\\left(x^{-6}y^{3}z^{5}\\right)$ and $\\left(x^{4}z^{5}+y^{8}z^{-7}\\right)$?

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

Choice D is correct. The product of $\\left(x^{-6}y^{3}z^{5}\\right)$ and $\\left(x^{4}z^{5}+y^{8}z^{-7}\\right)$ can be represented by the expression $\\left(x^{-6}y^{3}z^{5}\\right)\\left(x^{4}z^{5}+y^{8}z^{-7}\\right)$. Applying the distributive property to this expression yields $\\left(x^{-6}y^{3}z^{5}\\right)\\left(x^{4}z^{5}\\right)+\\left(x^{-6}y^{3}z^{5} \\right)\\left(y^{8}z^{-7}\\right)$, or $x^{-6}x^{4}y^{3}z^{5}z^{5}+x^{-6}y^{3}y^{8}z^{5}z^{-7}$. This expression is equivalent to $x^{-6+4}y^{3}z^{5+5}+x^{-6}y^{3+8}z^{5-7}$, or $x^{-2}y^{3}z^{10}+x^{-6}y^{11}z^{-2}$.

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

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

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

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

Which expression represents the product of $\\left(x^{-6}y^{3}z^{5}\\right)$ and $\\left(x^{4}z^{5}+y^{8}z^{-7}\\right)$?

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

$x^{-2}z^{10}+y^{11}z^{-2}$

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

$x^{-2}z^{10}+x^{-6}z^{-2}$

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

$x^{-2}y^{3}z^{10}+y^{8}z^{-7}$

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

$x^{-2}y^{3}z^{10}+x^{-6}y^{11}z^{-2}$

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

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

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

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

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-advanced-math-multiple-choice-question-160"}

Which expression represents the product of $\left(x^{-6}y^{3}z^{5}\right)$ and $\left(x^{4}z^{5}+y^{8}z^{-7}\right)$?