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

The expression $\\frac{x^{-2}y^{\\frac{1}{2}}}{x^{\\frac{1}{3}}y^{-1}}$, where $x>1$ and $y>1$, is equivalent to which of the following?

","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-73"}],"about":{"@type":"Thing","name":"Math, Advanced Math, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Advanced Math","Duplicate"],"name":"

The expression $\\frac{x^{-2}y^{\\frac{1}{2}}}{x^{\\frac{1}{3}}y^{-1}}$, where $x>1$ and $y>1$, is equivalent to which of the following?

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

Choice D is correct. For $x>1$ and $y>1$, $x^{\\frac{1}{3}}$ and $y^{\\frac{1}{2}}$ are equivalent to $\\sqrt[3]{x}$ and $\\sqrt[3]{y}$, respectively. Also, $x^{-2}$ and $y^{-1}$ are equivalent to $\\frac{1}{x^{2}}$ and $\\frac{1}{y}$, respectively. Therefore, the given expression can be rewritten as $\\frac{y\\sqrt{y}}{x^{2}\\sqrt[3]{x}}$.

Choices A, B, and C are incorrect because these choices are not equivalent to the given expression for $x>1$ and $y>1$.

For example, for $x=2$ and $y=2$, the value of the given expression is $2^{-\\frac{5}{6}}$; the values of the choices, however, are $2^{-\\frac{1}{3}}$, $2^\\frac{5}{6}$, and 1, respectively.

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

The expression $\\frac{x^{-2}y^{\\frac{1}{2}}}{x^{\\frac{1}{3}}y^{-1}}$, where $x>1$ and $y>1$, is equivalent to which of the following?

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

$\\frac{\\sqrt{y}}{\\sqrt[3]{x^{2}}}$

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

$\\frac{y\\sqrt{y}}{\\sqrt[3]{x^{2}}}$

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

$\\frac{y\\sqrt{y}}{x\\sqrt{x}}$

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

$\\frac{y\\sqrt{y}}{x^{2}\\sqrt[3]{x}}$

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

Choices A, B, and C are incorrect because these choices are not equivalent to the given expression for $x>1$ and $y>1$.

For example, for $x=2$ and $y=2$, the value of the given expression is $2^{-\\frac{5}{6}}$; the values of the choices, however, are $2^{-\\frac{1}{3}}$, $2^\\frac{5}{6}$, and 1, respectively.

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

Choices A, B, and C are incorrect because these choices are not equivalent to the given expression for $x>1$ and $y>1$.

For example, for $x=2$ and $y=2$, the value of the given expression is $2^{-\\frac{5}{6}}$; the values of the choices, however, are $2^{-\\frac{1}{3}}$, $2^\\frac{5}{6}$, and 1, respectively.

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-advanced-math-multiple-choice-question-73"}

The expression $\frac{x^{-2}y^{\frac{1}{2}}}{x^{\frac{1}{3}}y^{-1}}$, where $x>1$ and $y>1$, is equivalent to which of the following?