{"id":"cb_practice_pdf:t4-math-m1-q21","source_id":"cb_practice_pdf","source_item_id":"t4-math-m1-q21","external_id":null,"ibn":null,"question_id":null,"program":"SAT","module":"math","domain_code":null,"domain":null,"skill_code":null,"skill":null,"difficulty":null,"score_band":null,"answer_type":"spr","answer_source":"rationale","layout_warning":null,"form_id":"cb_practice_pdf:test-4","module_number":1,"position":21,"stem":"5 The expression 6^5 3 x^45 ·^8 2^8 x is equivalent to ax^b, > 1 where a and b are positive constants and x. What is the value of a + b?","stimulus":"","stimulus_html":null,"stem_html":"<p>5 The expression 6^5 3 x^45 ·^8 2^8 x is equivalent to ax^b, &gt; 1 where a and b are positive constants and x. What is the value of a + b?</p>","rationale_html":"<p>m The correct answer is 361 . The rational exponent property is n y m= yn, where 8 &gt; &gt; y 0, m and n are integers, and n 0. This property can be applied to rewrite ( )( )( )( ) ( ) the given expression 6 5 3 5 x 45  8 2 8 x as 6 3 5 5 x 4 5 5 28 8 x8 1 , or 6 ( 3 )( x 9 )( 2 ) x8 1 . This expression can be rewritten by multiplying the constants, which gives ( ) 36 ( x 9 ) x8 1 . The multiplication exponent property is y n  y m= y n + m , where y &gt; 0. ( ) ( ) 1 9 +1 This property can be applied to rewrite the expression 36 x 9 x8 as 36x 8, or 73 73 36x8. Therefore, 6 5 3 5 x 45  8 2 8 x = 36x8. It’s given that 6 5 3 5 x 45  8 2 8 x is b = =73 + = +73 equivalent to ax ; therefore, a 36 and b . It follows that a b 36 . 8 8 Finding a common denominator on the right-hand side of this equation gives + =288+73 + =361 a b , or a b . Note that 361/8, 45.12, and 45.13 are examples of 8 8 8 ways to enter a correct answer.</p>","correct_answer":["361"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[],"attribution":{"source_id":"cb_practice_pdf","source_name":"College Board full-length SAT practice tests (PDF)","rights_holder":"College Board","canonical_url":"https://satsuite.collegeboard.org/practice/practice-tests/paper","retrieved_from":"https://satsuite.collegeboard.org/practice/practice-tests/paper","attribution":"Full-length SAT practice tests 4–11 © College Board, published free at satsuite.collegeboard.org.","disclaimer":"Extracted from PDF layout: equations, figures and tables do not survive intact. Use the original PDFs for anything the text renders poorly. SAT® is a trademark registered by the College Board, which is not affiliated with and does not endorse this project.","license":"College Board copyright. Free to download; not licensed for redistribution.","redistributable":false,"item_count":905}}