{"id":"cb_question_bank:d01a3601-ee61-4c52-a0aa-5b5bd7756d06","source_id":"cb_question_bank","source_item_id":"d01a3601-ee61-4c52-a0aa-5b5bd7756d06","external_id":null,"ibn":"025800-DC","question_id":"0b3d25c5","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 of the following is equivalent to the fourth root of, x squared, plus 8 x, plus 16, end root , where x is greater than 0 ?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">Which of the following is equivalent to <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/09956661a5f420cead05f5c15cfacf373a26be2604b52ed7e2a5f7cefc5af09d\" alt=\"the fourth root of, x squared, plus 8 x, plus 16, end root\"></span></span>, where <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6ca09b244cb4a0414885894bc1ac4e0242305210b23d08ccb20204e38d574daf\" alt=\"x is greater than 0\"></span></span>?</p>\n","rationale_html":"<p>Choice D is correct. The given expression can also be written as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6bf427f0218d15f7b450a70a68b18be0b13bda838915dcf18bf974015d07ea64\" alt=\"open parenthesis, x squared, plus 8, x, plus 16, close parenthesis, raised to the one fourth power\"></span>. The trinomial <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/eec59c78b5c3973163bff196da8a36d8569b2e862ab852cd86b396b5ab7dc315\" alt=\"x squared, plus 8, x, plus 16 \"></span> can be rewritten in factored form as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c199d9751ea70ac581252c9ca7395c5b7a3fd6f5a6628065a2f62228da9bc4cb\" alt=\"open parenthesis, x plus 4, close parenthesis, squared\"></span>. Thus, the entire expression can be rewritten as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/92eae9b67b11fe5be4889d4bf222ba2d4ce4bc6ab1f2e978fd63083d086fb7a2\" alt=\"open parenthesis, open parenthesis, x plus 4, close parenthesis, squared, close parenthesis, raised to the one fourth power\"></span>. Simplifying the exponents yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/4ad3523b821f017c469a3e15a5b2dcfb6fe2820c4fed2c3b6b3fa9e80951b235\" alt=\"open parenthesis, x plus 4, close parenthesis, raised to the one half power\"></span>.</p><p>Choices A, B, and C are incorrect and may result from errors made when simplifying the exponents in the expression <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/92eae9b67b11fe5be4889d4bf222ba2d4ce4bc6ab1f2e978fd63083d086fb7a2\" alt=\"open parenthesis, open parenthesis, x plus 4, close parenthesis, squared, close parenthesis, raised to the one fourth power\"></span>.</p><p></p>\n","correct_answer":["D"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.619000+00:00","source_updated_at":"2023-08-02T20:25:59.619000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/1ad82bc453d3581b421d1b14a289316fb4efd350440a723a4c96b439aafaeaee\" alt=\"open parenthesis, x plus 4, close parenthesis, to the fourth power\"></span></span>\n          </p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c199d9751ea70ac581252c9ca7395c5b7a3fd6f5a6628065a2f62228da9bc4cb\" alt=\"open parenthesis, x plus 4, close parenthesis, squared\"></span></span>\n          </p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8ba69b270fef856d4aa9d37425544f479a6418f4c92f631664ab4feb7d62f4c3\" alt=\"open parenthesis, x plus 4, close parenthesis\"></span></p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/4ad3523b821f017c469a3e15a5b2dcfb6fe2820c4fed2c3b6b3fa9e80951b235\" alt=\"open parenthesis, x plus 4, close parenthesis, raised to the one half power\"></span></span>\n          </p>\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}}