SOLUTION: {{{(7 * 10^3)*(8 * 10^-9)}}} Please Help if you can, and please show your work. Thank You

Algebra ->  Exponents -> SOLUTION: {{{(7 * 10^3)*(8 * 10^-9)}}} Please Help if you can, and please show your work. Thank You      Log On


   

Question 186906: %287+%2A+10%5E3%29%2A%288+%2A+10%5E-9%29
Please Help if you can, and please show your work.
Thank You
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
%287+%2A+10%5E3%29%2A%288+%2A+10%5E-9%29
This are 4 different factors, and they can be
placed in any order without changing the
expression
7%2A8%2A10%5E3%2A10%5E-9
56%2A10%5E3%2A10%5E-9
The general rule for negative exponents is:
a%5E%28-b%29+=+1%2F%28a%5Eb%29
another rule is:
a%5Eb%2Aa%5E%28-c%29+=+a%5E%28b-c%29
In this problem:
10%5E-9+=+1%2F1000000000
10%5E3+=+1000
------------------
10%5E3%2A10%5E-9+=+1000+%2A+%281%2F1000000000%29
1000+%2A+%281%2F1000000000%29+=+1%2F1000000
1%2F1000000+=+10%5E-6, so you see that
10%5E3%2A10%5E-9+=+10%5E%283-9%29
10%5E%283-9%29+=+10%5E-6
So, the whole answer is
56%2A10%5E-6