{"id":"cb_question_bank:392d3aee-f776-4873-b514-343a1d43bd17","source_id":"cb_question_bank","source_item_id":"392d3aee-f776-4873-b514-343a1d43bd17","external_id":null,"ibn":"08126-DC","question_id":"a520ba07","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.A.","skill":"Equivalent expressions","difficulty":"M","score_band":4,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Which of the following expressions is equivalent to the expression above?","stimulus":"the cube root of x to the power 3, times y to the power 6, end root","stimulus_html":"<div class=\"stimulus_reference \">\n        <p class=\"standalone_statement style:1 \">\n          <span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b2463e6d58c8b5f88b33ea497343aae944a8893bcdf8cd01fe0de7fe095ee78d\" alt=\"the cube root of x to the power 3, times y to the power 6, end root\"></span></span>\n        </p>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">Which of the following expressions is equivalent to the expression above?</p>\n","rationale_html":"<p>Choice B is correct. One of the properties of radicals is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ab9c594b40640c2f81411f913c6b36a20c954afda294cc62dc4c9ae4e169b71a\" alt=\"the nth root of a times b, end root, equals the nth root of a, end root, times the nth root of b, end root\"></span>. Thus, the given expression can be rewritten as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5be64730c88db6fcc37bff13c6f48014acbf94616accd67a6cf47919d5be1435\" alt=\"the cube root of x cubed, end root, times the cube root of y to the power 6, end root\"></span>. Simplifying by taking the cube root of each part gives <span class=\"italic\">x</span><sup>1 </sup><span class=\"italic\">⋅ y</span><sup>2</sup>, or <span class=\"italic\">xy</span><sup>2</sup>.</p><p>Choices A, C, and D are incorrect and may be the result of incorrect application of the properties of exponents and radicals.</p><p></p>\n","correct_answer":["B"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.634000+00:00","source_updated_at":"2023-08-02T20:25:59.634000+00:00","options":[{"label":"A","content_html":"<span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8dfebc48d5eb8ba0027a39fbbcce07b65e274b2d7d101e1206b4b1a6c00cd116\" alt=\"y squared\"></span></span>\n","ord":0},{"label":"B","content_html":"<span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f23f04427a46c2d962ad0a9b30f711e0dc155806161a770351b50ce1764d9014\" alt=\"x times y squared\"></span></span>\n","ord":1},{"label":"C","content_html":"<span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/06083b6b0bbea21f2ce78b805c140399f27e30fc7c8374776410b4f11683149d\" alt=\"y cubed\"></span></span>\n","ord":2},{"label":"D","content_html":"<span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/683edf9fec1df0859bf8f7004a1be8dde4e772e6ad8e28df1f46de3b30c3fb6d\" alt=\"x times y cubed\"></span></span>\n","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}}