{"id":"cb_question_bank:152723d6-f626-4135-9304-8a5dea47517c","source_id":"cb_question_bank","source_item_id":"152723d6-f626-4135-9304-8a5dea47517c","external_id":null,"ibn":"070622-DC","question_id":"40c09d66","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.A.","skill":"Equivalent expressions","difficulty":"H","score_band":7,"answer_type":"spr","answer_source":"rationale","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"If the fraction with numerator the square root of x to the fifth power, end root, and denominator the cube root of x to the fourth power, end root, end fraction, equals x raised to the fraction a over b power for all positive values of x , what is the value of the fraction a over b ?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">If <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/66c25cebf3e19ef16c46431decce7c24ca3d146c958b2b77242bd6115660be5b\" alt=\"the fraction with numerator the square root of x to the fifth power, end root, and denominator the cube root of x to the fourth power, end root, end fraction, equals x raised to the fraction a over b power \"></span></span> for all positive values of <span class=\"italic\">x</span>, what is the value of <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5cf6d5a41f6c0c6acf669bc86eac17f43cffafdb4d96ee9a04d1ef02f49619a7\" alt=\"the fraction a over b\"></span></span>?</p>\n","rationale_html":"<p>The correct answer is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/56c1df4dad8bd2f498c024d45f1cae610b65d1c08ddd6e82af10b17cabe6b074\" alt=\"7 over 6\"></span>. The value of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5cf6d5a41f6c0c6acf669bc86eac17f43cffafdb4d96ee9a04d1ef02f49619a7\" alt=\"a, over b \"></span> can be found by first rewriting the left-hand side of the given equation as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b652575ecae13f4f3f2561da245899fa031c948b75b1db258388201a4c909f38\" alt=\"the fraction with numerator x raised to the five halves power, and denominator x raised to the four thirds power, end fraction \"></span>. Using the properties of exponents, this expression can be rewritten as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/51f1c0e68d00f30177c35e6a27bbd1a5cd12d6a4f165d1105dcaa7b4b2f1bae0\" alt=\"x raised to the open parenthesis, five halves, minus four thirds, close parenthesis, power\"></span>. This expression can be rewritten by subtracting the fractions in the exponent, which yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e537c5d55af3d8aa8b8bcafd2c0bb0c4da81bbb21eea2f7b4f993eb14a1482d6\" alt=\"x raised to the fraction 7 over 6, power\"></span>. Thus, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5cf6d5a41f6c0c6acf669bc86eac17f43cffafdb4d96ee9a04d1ef02f49619a7\" alt=\"a, over b \"></span> is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/56c1df4dad8bd2f498c024d45f1cae610b65d1c08ddd6e82af10b17cabe6b074\" alt=\"7 over 6\"></span>. Note that 7/6, 1.166, and 1.167 are examples of ways to enter a correct answer.</p>\n","correct_answer":["7"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.631000+00:00","source_updated_at":"2023-08-02T20:25:59.631000+00:00","options":[],"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}}