SOLUTION: Show all work. Find the exact value of n. {{{3^2002 - 3^2001 + 3^2000 - 3^1999 = n(3^1999)}}}

Algebra ->  Exponents -> SOLUTION: Show all work. Find the exact value of n. {{{3^2002 - 3^2001 + 3^2000 - 3^1999 = n(3^1999)}}}      Log On


   

Question 1129938: Show all work. Find the exact value of n.
3%5E2002+-+3%5E2001+%2B+3%5E2000+-+3%5E1999+=+n%283%5E1999%29
Answer by greenestamps(13334) About Me  (Show Source):
You can put this solution on YOUR website!


Factor 3^1999 out of each term on the left....

3%5E2002+-+3%5E2001+%2B+3%5E2000+-+3%5E1999 =

%283%5E3%29%2A3%5E1999+-+%283%5E2%29%2A3%5E1999+%2B+3%2A3%5E1999+-+1%2A3%5E1999 =

%2827-9%2B3-1%29%2A3%5E1999 =

20%283%5E1999%29

ANSWER: n = 20