tag:blogger.com,1999:blog-5134418801703349975.post7710185164301402147..comments2023-05-12T11:17:29.120-04:00Comments on Math Arguments: 147: ExponentsCurmudgeonhttp://www.blogger.com/profile/04323026187622872114noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-5134418801703349975.post-9083692642151113122014-06-09T11:24:06.988-04:002014-06-09T11:24:06.988-04:00I believe the only allowable possibilities are
(2...I believe the only allowable possibilities are<br /><br />(2^2)^6 = (2^3)^4 = (2^4)^3 = (2^6)^2<br /><br />Since the only prime factor of 2^12 is 2, the same must be true for b, and the only ways to write 12 as an ordered product of integers greater than 1 is<br /><br />(2)(6) = (3)(4) = (4)(3) = (6)(2)<br /><br />In other words, the possibilities are:<br /><br />1. a = 2^2 = 4 and b = 6<br /><br />2. a = 2^3 = 8 and b = 4<br /><br />3. a = 2^4 = 16 and b = 3<br /><br />4. a = 2^6 = 64 and b = 2Dave L. Renfrohttps://www.blogger.com/profile/00863074796446784081noreply@blogger.comtag:blogger.com,1999:blog-5134418801703349975.post-53440812920174356242014-06-09T11:18:56.803-04:002014-06-09T11:18:56.803-04:00This comment has been removed by the author.Dave L. Renfrohttps://www.blogger.com/profile/00863074796446784081noreply@blogger.comtag:blogger.com,1999:blog-5134418801703349975.post-12424459435734746922014-06-08T03:41:11.505-04:002014-06-08T03:41:11.505-04:00I want to say 8 but that seems too obvious to me. ...I want to say 8 but that seems too obvious to me. Have I missed something?Petehttps://www.blogger.com/profile/17698997955275253046noreply@blogger.com