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## by Matteo Tamburini on May 24, 2010

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• 5)
• 5)
• I am looking for a number that times itself five times gives -38880
• 5)
• I am looking for a number that times itself five times gives -38880
• Notice that there is such a number:
• 5)
• I am looking for a number that times itself five times gives -38880
• Notice that there is such a number: the product (multiplication) of five negative numbers is a negative number
• 5)
• I am looking for a number that times itself five times gives -38880
• I’ll make a list of “perfect fifth powers”
• 5)
• I am looking for a number that times itself five times gives -38880
• I’ll make a list of “perfect fifth powers”
• 2 5 = 32;
• 5)
• I am looking for a number that times itself five times gives -38880
• I’ll make a list of “perfect fifth powers”
• 2 5 = 32;
• 3 5 = 243;
• 5)
• I am looking for a number that times itself five times gives -38880
• I’ll make a list of “perfect fifth powers”
• 2 5 = 32;
• 3 5 = 243;
• 4 5 = 1024;
• 5)
• I am looking for a number that times itself five times gives -38880
• I’ll make a list of “perfect fifth powers”
• 2 5 = 32;
• 3 5 = 243;
• 4 5 = 1024;
• 5 5 = 3125;
• 5)
• I am looking for a number that times itself five times gives -38880
• I’ll make a list of “perfect fifth powers”
• 2 5 = 32;
• 3 5 = 243;
• 4 5 = 1024;
• 5 5 = 3125;
• 6 5 = 7776
• 5)
• I am looking for a number that times itself five times gives -38880
• I’ll make a list of “perfect fifth powers”
• 2 5 = 32;
• 3 5 = 243; Now I’ll see if any of these
• 4 5 = 1024; go evenly into -38880
• 5 5 = 3125;
• 6 5 = 7776
• 5)
• I am looking for a number that times itself five times gives -38880
• -38880/32 = 1215
• 5)
• I am looking for a number that times itself five times gives -38880
• -38880/32 = 1215 yes!
• 5)
• I am looking for a number that times itself five times gives -38880
• -38880/32 = 1215
• -38880/243 = 160
• 5)
• I am looking for a number that times itself five times gives -38880
• -38880/32 = 1215
• -38880/243 = 160 yes!
• 5)
• I am looking for a number that times itself five times gives -38880
• -38880/32 = 1215
• -38880/243 = 160
• 5)
• I am looking for a number that times itself five times gives -38880
• -38880/32 = 1215
• -38880/243 = 160
• -38880/1024 = 37.96…
• 5)
• I am looking for a number that times itself five times gives -38880
• -38880/32 = 1215
• -38880/243 = 160
• -38880/1024 = 37.96… no
• 5)
• I am looking for a number that times itself five times gives -38880
• -38880/32 = 1215
• -38880/243 = 160
• -38880/1024 = 37.96…
• -38880/3125 = 12.44…
• 5)
• I am looking for a number that times itself five times gives -38880
• -38880/32 = 1215
• -38880/243 = 160
• -38880/1024 = 37.96…
• -38880/3125 = 12.44… no
• 5)
• I am looking for a number that times itself five times gives -38880
• -38880/32 = 1215
• -38880/243 = 160
• -38880/1024 = 37.96…
• -38880/3125 = 12.44…
• -38880/7776 = 5
• 5)
• I am looking for a number that times itself five times gives -38880
• -38880/32 = 1215
• -38880/243 = 160
• -38880/1024 = 37.96…
• -38880/3125 = 12.44…
• -38880/7776 = 5 yes!
• 5)
• I am looking for a number that times itself five times gives -38880
• -38880/32 = 1215 Among these,
• -38880/243 = 160 I’m going to
• -38880/1024 = 37.96… choose the
• -38880/3125 = 12.44… largest number
• -38880/7776 = 5 yes!
• 5)
• So now let me write -38880 as -7776*5
• 5)
• So now let me write -38880 as -7776*5
• 5)
• So now let me write -38880 as -7776*5
• 5)
• So now let me write -38880 as -7776*5
• Another example
• 17)
• 17)
• I think for now I’ll ignore the stuff outside of the parenthesis
• 17)
• I think for now I’ll ignore the stuff outside of the parenthesis and just consider
• 17)
• I think for now I’ll ignore the stuff outside of the parenthesis and just consider
• This can also be reduced “one piece at a time”
• 17)
• I think for now I’ll ignore the stuff outside of the parenthesis and just consider
• This can also be reduced “one piece at a time”
• So first consider
• 17)
• I think for now I’ll ignore the stuff outside of the parenthesis and just consider
• This can also be reduced “one piece at a time”
• So first consider
• 2 4 = 16, and 16 goes evenly into 32
• 17)
• I think for now I’ll ignore the stuff outside of the parenthesis and just consider
• This can also be reduced “one piece at a time”
• So first consider
• 2 4 = 16, and 16 goes evenly into 32
• So write
• 17)
• I think for now I’ll ignore the stuff outside of the parenthesis and just consider
• This can also be reduced “one piece at a time”
• So first consider
• 2 4 = 16, and 16 goes evenly into 32
• So write 
• 17)
• I think for now I’ll ignore the stuff outside of the parenthesis and just consider
• This can also be reduced “one piece at a time”
• So first consider
• 2 4 = 16, and 16 goes evenly into 32
• So write  
• 17)
• I think for now I’ll ignore the stuff outside of the parenthesis and just consider
• This can also be reduced “one piece at a time”
• So first consider
• 2 4 = 16, and 16 goes evenly into 32
• So write   
• 17)
• I think for now I’ll ignore the stuff outside of the parenthesis and just consider
• This can also be reduced “one piece at a time”
• So first consider
• 2 4 = 16, and 16 goes evenly into 32
• So write   
• 17)
• I think for now I’ll ignore the stuff outside of the parenthesis and just consider
• This can also be reduced “one piece at a time”
• Now consider
• 17)
• I think for now I’ll ignore the stuff outside of the parenthesis and just consider
• This can also be reduced “one piece at a time”
• Now consider
• I can break it up as
• 17)
• I think for now I’ll ignore the stuff outside of the parenthesis and just consider
• This can also be reduced “one piece at a time”
• Now consider
• I can break it up as
• Which is the same as
• 17)
• I think for now I’ll ignore the stuff outside of the parenthesis and just consider
• This can also be reduced “one piece at a time”
• Now consider
• I can break it up as
• Which is the same as
• And finally, this is the same as
• 17)
• I think for now I’ll ignore the stuff outside of the parenthesis and just consider
• This can also be reduced “one piece at a time”
• Now consider
• I can break it up as
• Which is the same as
• And finally, this is the same as
• 17)
• I think for now I’ll ignore the stuff outside of the parenthesis and just consider
• This can also be reduced “one piece at a time”
• Now consider
• 17)
• I think for now I’ll ignore the stuff outside of the parenthesis and just consider
• This can also be reduced “one piece at a time”
• Now consider
• I can break it up as
• 17)
• I think for now I’ll ignore the stuff outside of the parenthesis and just consider
• This can also be reduced “one piece at a time”
• Now consider
• I can break it up as
• Which is the same as
• 17)
• I think for now I’ll ignore the stuff outside of the parenthesis and just consider
• This can also be reduced “one piece at a time”
• Now consider
• I can break it up as
• Which is the same as
• And finally, this is the same as
• 17)
• I think for now I’ll ignore the stuff outside of the parenthesis and just consider
• This can also be reduced “one piece at a time”
• Now consider
• I can break it up as
• Which is the same as
• And finally, this is the same as
• 17)
• I think for now I’ll ignore the stuff outside of the parenthesis and just consider
• So is the same as
• 17)
• I think for now I’ll ignore the stuff outside of the parenthesis and just consider
• So is the same as
• And is the same as
• 17)
• I think for now I’ll ignore the stuff outside of the parenthesis and just consider
• So is the same as
• And is the same as
• And is the same as
• 17)
• I think for now I’ll ignore the stuff outside of the parenthesis and just consider
• So is the same as
• And is the same as
• And is the same as
• 17)
• I think for now I’ll ignore the stuff outside of the parenthesis and just consider
• So is the same as
• And is the same as
• And is the same as
• So OUTSIDE the root I get 2ab
• 17)
• I think for now I’ll ignore the stuff outside of the parenthesis and just consider
• So is the same as
• And is the same as
• And is the same as
• And INSIDE the root I get 2ab 2
• 17)
• This tells us that
• 17)
• This tells us that
• is the same as
• 17)
• This tells us that
• is the same as
• And now we’ll take into account the ab on the outside of the root
• 17)
• This tells us that
• is the same as
• And now we’ll take into account the ab on the outside of the root and we can say that
• 17)
• This tells us that
• is the same as
• And now we’ll take into account the ab on the outside of the root and we can say that
• is the same as