{"id":"cb_question_bank:c0b242dc-df3d-402c-ae93-5e9d71da54fe","source_id":"cb_question_bank","source_item_id":"c0b242dc-df3d-402c-ae93-5e9d71da54fe","external_id":"e7cb9147-ae39-47e9-a4cb-da0cfbf0b250","ibn":null,"question_id":"b74f2feb","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":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The expression 6 RootIndex 5 StartRoot 3 Superscript 5 Baseline x Superscript 45 Baseline EndRoot dot RootIndex 8 StartRoot 2 Superscript 8 Baseline x EndRoot is equivalent to a x Superscript b , where a and b are positive constants and x greater than 1 . What is the value of a plus b ?","stimulus":"","stimulus_html":null,"stem_html":"

The expression 635x455·28x8 is equivalent to \n\ta\n\t\n\t\tx\n\t\tb\n\t\n\n, where a\n and b\n are positive constants and x>1. What is the value of \n\ta\n\t+\n\tb\n\n?

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The correct answer is 3618. The rational exponent property is ymn=ymn, where y>0, m\n and n\n are integers, and n>0. This property can be applied to rewrite the given expression 635x455·28x8 as 6355x455288x18, or 63x92x18. This expression can be rewritten by multiplying the constants, which gives 36x9x18. The multiplication exponent property is yn·ym=yn+m, where y>0. This property can be applied to rewrite the expression 36x9x18 as 36x9+18, or 36x738. Therefore, 635x455·28x8=36x738. It's given that 635x455·28x8 is equivalent to axb; therefore, a=36 and b=738. It follows that a+b=36+738. Finding a common denominator on the right-hand side of this equation gives a+b=2888+738, or a+b=3618. Note that 361/8, 45.12, and 45.13 are examples of ways to enter a correct answer.

","correct_answer":["361/8","45.12","45.13"],"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":[],"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}}