{"id":"cb_question_bank:3e785172-08ab-46ec-840e-16cb83c67899","source_id":"cb_question_bank","source_item_id":"3e785172-08ab-46ec-840e-16cb83c67899","external_id":null,"ibn":"026581-DC","question_id":"463eec13","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":"If x is not equal to 0 , which of the following expressions is equivalent to the fraction with numerator the square root of 16 x to the fourth power, y to the eighth power, end root, and denominator x cubed, end fraction ?","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/3a8feb6b8a5c68d9d3b2b44d6e4b37d4940b22cb96682ae384ec230480c81c6f\" alt=\"x is not equal to 0\"></span></span>, which of the following expressions is equivalent to <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5c38e7ee27d3eb83d4ae7c859ba8cc700f2a59b0e8d57224d9ae6c7eec2afef1\" alt=\"the fraction with numerator the square root of 16 x to the fourth power, y to the eighth power, end root, and denominator x cubed, end fraction\"></span></span> ?</p>\n","rationale_html":"<p>Choice D is correct. Taking the square root of an exponential expression halves the exponent, so <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/2a370ed8dbb2ec74d9702d21c1e104ef7de86765bb4cce1fc5b0bd5e2273e104\" alt=\"the fraction with numerator the square root of, 16 x to the fourth power times y to the eighth power, end root, and denominator x cubed, end fraction, equals, the fraction with numerator 4 x squared, times y to the fourth power, and denominator x cubed\"></span>, which further reduces to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/4f57ae6328d7b4aa98d1755fddae4f4e444adc44e19bf6cc590b77f85a4bdbe0\" alt=\"the fraction with numerator 4, y to the fourth power, and denominator x\"></span>. This can be rewritten as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/885bdb49e25916d0b72249a99f61f576fed79e70e7da8238f41ca2f1229a1cd1\" alt=\"4, x to the negative 1 power, times y to the fourth power\"></span>.</p><p>Choice A is incorrect and may result from neglecting the denominator of the given expression and from incorrectly calculating the square root of 16. Choice B is incorrect and may result from rewriting <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/9672a9958d9fd2aae42f6152cb12bb99e82ea4b06a7f99d5c9b2c4d2c51c8b60\" alt=\"1 over x\"></span> as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/dc3a6efe9f9296be60124648b48e9d3f93591e4238cc0218aeca04569bc1c0da\" alt=\"x to the first power\"></span> rather than <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/38bc2927cc1c7d781f17c05ad14727cd21405502dba5bd7e94e2329c1764af0f\" alt=\"x to the negative 1 power\"></span>. Choice C is incorrect and may result from taking the square root of the variables in the numerator twice instead of once.</p><p></p>\n","correct_answer":["D"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.620000+00:00","source_updated_at":"2023-08-02T20:25:59.620000+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/f0b070e27f8ce22dcbe0e8de000461ee6577812f83aa4a4628f2e42dcb5bb90e\" alt=\"8 x squared, y 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/82491518435cec31cd1bdc6e2a06c27faf6dc1bbffce4c9600ee9557c4e93a99\" alt=\"4 x, y to the fourth power\"></span></span>\n          </p>\n","ord":1},{"label":"C","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/a5189abe91a0909952890b7933c2e7037226452619b3df246a88495bdb7f7c5b\" alt=\"4 x raised to the negative 2 power, y squared\"></span></span>\n          </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/885bdb49e25916d0b72249a99f61f576fed79e70e7da8238f41ca2f1229a1cd1\" alt=\"4 x raised to the negative 1 power, y to the fourth 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}}