SOLUTION: please simplify the expression (4t)^-2 t^0/t^6v^-8 Thank you.

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Question 1060409:
please simplify the expression (4t)^-2 t^0/t^6v^-8
Thank you.
Found 3 solutions by CubeyThePenguin, MathTherapy, greenestamps:
Answer by CubeyThePenguin(3113) About Me  (Show Source):
You can put this solution on YOUR website!
(t/16)/(t^6 * v^(-8))
= %28v%5E8%29%2F%2816t%5E5%29

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!


please simplify the expression (4t)^-2 t^0/t^6v^-8
Thank you.
%284t%29%5E-2+%2A+t%5E0%2F%28t%5E6v%5E-+8%29 ====> %281%2F%284t%29%29%5E2+%2A+1%2F%28t%5E6v%5E-+8%29  ====> %281%2F%2816t%5E2%29%29%2F%28t%5E6v%5E-+8%29  ====> matrix%281%2C3%2C+1%2F%2816t%5E2%29%2C+%22%2A%22%2C+1%2F%28t%5E6v%5E-+8%29%29  ====> highlight_green%28v%5E8%2F%2816t%5E8%29%29

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


There are dozens of different paths for simplifying this expression. The other tutor has shown one perfectly good path.

I prefer to get rid of the negative exponents immediately; that avoids having fractions within the fraction -- e.g., 1%2F%284x%29%5E2+=+1%2F16x%5E2 in the numerator of the expression. So my path to the simplified expression would look something like this:

%284t%29%5E%28-2%29+t%5E0%2F%28t%5E6v%5E%28-8%29%29 --> t%5E0v%5E8%2F%28%284t%29%5E2%28t%5E6%29%29 --> %281%29v%5E8%2F%28%2816t%5E2%29%28t%5E6%29%29 --> v%5E8%2F16t%5E8

Try simplifying expressions like this in different ways and find the way that you find easiest for you.