{"id":"cb_question_bank:f0b83e7a-34aa-4196-b081-3b114f36d86c","source_id":"cb_question_bank","source_item_id":"f0b83e7a-34aa-4196-b081-3b114f36d86c","external_id":"34c2743d-443b-43f9-ad72-c43601418315","ibn":null,"question_id":"4eaf0a3a","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.A.","skill":"Equivalent expressions","difficulty":"M","score_band":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Which expression is equivalent to RootIndex 7 StartRoot x Superscript 9 Baseline y Superscript 9 Baseline EndRoot , where x and y are positive?","stimulus":"","stimulus_html":null,"stem_html":"<p>Which expression is equivalent to <math alttext=\"RootIndex 7 StartRoot x Superscript 9 Baseline y Superscript 9 Baseline EndRoot\"><mroot>\n\t<mrow>\n\t\t<msup>\n\t\t\t<mi>x</mi>\n\t\t\t<mn>9</mn>\n\t\t</msup>\n\t\t<msup>\n\t\t\t<mi>y</mi>\n\t\t\t<mn>9</mn>\n\t\t</msup>\n\t</mrow>\n\t<mn>7</mn>\n</mroot>\n</math>, where <math alttext=\"x\"><mi>x</mi>\n</math> and <math alttext=\"y\"><mi>y</mi>\n</math> are positive?</p>","rationale_html":"<p>Choice B is correct. For positive values of <math alttext=\"a\"><mi>a</mi>\n</math> and <math alttext=\"b\"><mi>b</mi>\n</math>, <math alttext=\"a Superscript m Baseline b Superscript m Baseline equals left parenthesis a b right parenthesis Superscript m\"><msup><mi>a</mi><mi>m</mi></msup><msup><mi>b</mi><mi>m</mi></msup><mo>=</mo><msup><mfenced><mrow><mi>a</mi><mi>b</mi></mrow></mfenced><mi>m</mi></msup></math>, <math alttext=\"RootIndex n StartRoot a EndRoot equals left parenthesis a right parenthesis Superscript StartFraction 1 Over n EndFraction\"><mroot><mi>a</mi><mi>n</mi></mroot><mo>=</mo><msup><mfenced><mi>a</mi></mfenced><mfrac><mn>1</mn><mi>n</mi></mfrac></msup></math>, and&nbsp;<math alttext=\"left parenthesis a Superscript j Baseline right parenthesis Superscript k Baseline equals a Superscript j k\"><msup><mfenced><msup><mi>a</mi><mi>j</mi></msup></mfenced><mi>k</mi></msup><mo>=</mo><msup><mi>a</mi><mrow><mi>j</mi><mi>k</mi></mrow></msup></math>. Therefore, the given expression,&nbsp;<math alttext=\"RootIndex 7 StartRoot x Superscript 9 Baseline y Superscript 9 Baseline EndRoot\"><mroot><mrow><msup><mi>x</mi><mn>9</mn></msup><msup><mi>y</mi><mn>9</mn></msup></mrow><mn>7</mn></mroot></math>, can be rewritten as&nbsp;<math alttext=\"RootIndex 7 StartRoot left parenthesis x y right parenthesis Superscript 9 Baseline EndRoot\"><mroot><msup><mfenced><mrow><mi>x</mi><mi>y</mi></mrow></mfenced><mn>9</mn></msup><mn>7</mn></mroot></math>. This expression is&nbsp;equivalent to <math alttext=\"left parenthesis left parenthesis x y right parenthesis Superscript 9 Baseline right parenthesis Superscript one seventh\"><msup><mfenced><msup><mfenced><mrow><mi>x</mi><mi>y</mi></mrow></mfenced><mn>9</mn></msup></mfenced><mfrac><mn>1</mn><mn>7</mn></mfrac></msup></math>, which can be rewritten as <math alttext=\"left parenthesis x y right parenthesis Superscript 9 dot one seventh\"><msup><mfenced><mrow><mi>x</mi><mi>y</mi></mrow></mfenced><mrow><mn>9</mn><mo>·</mo><mfrac><mn>1</mn><mn>7</mn></mfrac></mrow></msup></math>, or <math alttext=\"left parenthesis x y right parenthesis Superscript nine sevenths\"><msup><mfenced><mrow><mi>x</mi><mi>y</mi></mrow></mfenced><mfrac><mn>9</mn><mn>7</mn></mfrac></msup></math>.&nbsp;</p>\n<p>Choice A is incorrect and may result from conceptual or calculation errors.</p>\n<p>Choice C is incorrect and may result from conceptual or calculation errors.</p>\n<p>Choice D is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["B"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.821000+00:00","source_updated_at":"2023-08-02T20:25:59.821000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"left parenthesis x y right parenthesis Superscript seven ninths\"><msup><mfenced><mrow><mi>x</mi><mi>y</mi></mrow></mfenced><mfrac><mrow><mn>7</mn></mrow><mrow><mn>9</mn></mrow></mfrac></msup></math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"left parenthesis x y right parenthesis Superscript nine sevenths\"><msup><mfenced><mrow><mi>x</mi><mi>y</mi></mrow></mfenced><mfrac><mrow><mn>9</mn></mrow><mrow><mn>7</mn></mrow></mfrac></msup></math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"left parenthesis x y right parenthesis Superscript 16\"><msup><mfenced><mrow><mi>x</mi><mi>y</mi></mrow></mfenced><mrow><mn>16</mn></mrow></msup></math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"left parenthesis x y right parenthesis Superscript 63\"><msup><mfenced><mrow><mi>x</mi><mi>y</mi></mrow></mfenced><mrow><mn>63</mn></mrow></msup></math></p>","ord":3}],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}