{"id":"cb_question_bank:91741146-0613-4ab5-a2c0-7eadf0b6c07a","source_id":"cb_question_bank","source_item_id":"91741146-0613-4ab5-a2c0-7eadf0b6c07a","external_id":"4544da8e-b007-4229-a855-ce10c2bbf557","ibn":null,"question_id":"42f19012","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 a Superscript StartFraction 11 Over 12 EndFraction , where a greater than 0 ?","stimulus":"","stimulus_html":null,"stem_html":"<p>Which expression is equivalent to <math alttext=\"a Superscript StartFraction 11 Over 12 EndFraction\"><msup>\n\t<mi>a</mi>\n\t<mfrac>\n\t\t<mn>11</mn>\n\t\t<mn>12</mn>\n\t</mfrac>\n</msup>\n</math>, where <math alttext=\"a greater than 0\"><mi>a</mi><mo>&gt;</mo><mn>0</mn></math>?</p>","rationale_html":"<p>Choice B is correct. Since <math alttext=\"StartFraction 12 Over 12 EndFraction equals 1\"><mfrac><mn>12</mn><mn>12</mn></mfrac><mo>=</mo><mn>1</mn></math>, multiplying the exponent of the given expression by <math alttext=\"StartFraction 12 Over 12 EndFraction\"><mfrac><mn>12</mn><mn>12</mn></mfrac></math> yields an equivalent expression: <math alttext=\"a Superscript left parenthesis StartFraction 11 Over 12 EndFraction right parenthesis left parenthesis StartFraction 12 Over 12 EndFraction right parenthesis Baseline equals a Superscript left parenthesis StartFraction 132 Over 144 EndFraction right parenthesis\"><msup><mi>a</mi><mrow><mfenced><mfrac><mn>11</mn><mn>12</mn></mfrac></mfenced><mfenced><mfrac><mn>12</mn><mn>12</mn></mfrac></mfenced></mrow></msup><mo>=</mo><msup><mi>a</mi><mfenced><mfrac><mn>132</mn><mn>144</mn></mfrac></mfenced></msup></math>. Since&nbsp;<math alttext=\"StartFraction 132 Over 144 EndFraction equals 132 left parenthesis StartFraction 1 Over 144 EndFraction right parenthesis\"><mfrac><mn>132</mn><mn>144</mn></mfrac><mo>=</mo><mn>132</mn><mfenced><mfrac><mn>1</mn><mn>144</mn></mfrac></mfenced></math>, the expression&nbsp;<math alttext=\"a Superscript StartFraction 132 Over 144 EndFraction\"><msup><mi>a</mi><mfrac><mn>132</mn><mn>144</mn></mfrac></msup></math> can be rewritten as <math alttext=\"a Superscript left parenthesis 132 right parenthesis left parenthesis StartFraction 1 Over 144 EndFraction right parenthesis\"><msup><mi>a</mi><mrow><mfenced><mn>132</mn></mfenced><mfenced><mfrac><mn>1</mn><mn>144</mn></mfrac></mfenced></mrow></msup></math>. Applying properties of exponents, this expression can be rewritten as <math alttext=\"left parenthesis a Superscript 132 Baseline right parenthesis Superscript StartFraction 1 Over 144 EndFraction\"><msup><mfenced><msup><mi>a</mi><mn>132</mn></msup></mfenced><mfrac><mn>1</mn><mn>144</mn></mfrac></msup></math>. An expression of the form <math alttext=\"left parenthesis m right parenthesis Superscript StartFraction 1 Over k EndFraction\"><msup><mfenced><mi>m</mi></mfenced><mfrac><mn>1</mn><mi>k</mi></mfrac></msup></math>, where <math alttext=\"m greater than 0\"><mi>m</mi><mo>&gt;</mo><mn>0</mn></math> and <math alttext=\"k greater than 0\"><mi>k</mi><mo>&gt;</mo><mn>0</mn></math>, is equivalent to <math alttext=\"RootIndex k StartRoot m EndRoot\"><mroot><mi>m</mi><mi>k</mi></mroot></math>. Therefore, <math alttext=\"left parenthesis a Superscript 132 Baseline right parenthesis Superscript StartFraction 1 Over 144 EndFraction\"><msup><mfenced><msup><mi>a</mi><mn>132</mn></msup></mfenced><mfrac><mn>1</mn><mn>144</mn></mfrac></msup></math> is equivalent to <math alttext=\"RootIndex 144 StartRoot a Superscript 132 Baseline EndRoot\"><mroot><msup><mi>a</mi><mn>132</mn></msup><mn>144</mn></mroot></math>.</p>\n<p>Choice A is incorrect and may result from conceptual or calculation errors.&nbsp;</p>\n<p>Choice C is incorrect and may result from conceptual or calculation errors.&nbsp;</p>\n<p>Choice D is incorrect and may result from conceptual or calculation errors.&nbsp;</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=\"RootIndex 12 StartRoot a Superscript 132 Baseline EndRoot\"><mroot>\n\t<msup>\n\t\t<mi>a</mi>\n\t\t<mn>132</mn>\n\t</msup>\n\t<mn>12</mn>\n</mroot>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"RootIndex 144 StartRoot a Superscript 132 Baseline EndRoot\"><mroot>\n\t<msup>\n\t\t<mi>a</mi>\n\t\t<mn>132</mn>\n\t</msup>\n\t<mn>144</mn>\n</mroot>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"RootIndex 121 StartRoot a Superscript 132 Baseline EndRoot\"><mroot>\n\t<msup>\n\t\t<mi>a</mi>\n\t\t<mn>132</mn>\n\t</msup>\n\t<mn>121</mn>\n</mroot>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"RootIndex 11 StartRoot a Superscript 132 Baseline EndRoot\"><mroot>\n\t<msup>\n\t\t<mi>a</mi>\n\t\t<mn>132</mn>\n\t</msup>\n\t<mn>11</mn>\n</mroot>\n</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}}