SOLUTION: (3Y^4 n^6)^2/ (Y^2 n^-3)^4 please help me understand this

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Question 286726: (3Y^4 n^6)^2/ (Y^2 n^-3)^4 please help me understand this
Found 2 solutions by ichudov, richwmiller:
Answer by ichudov(507) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Graphical form: %283Y%5E4n%5E6%29%5E2%2F%28Y%5E2n%5E-3%29%5E4 simplifies to 3%2AY%5E2
  • Text form: (3Y^4n^6)^2/(Y^2n^-3)^4 simplifies to 3*Y^2
  • Cartoon (animation) form: simplify_cartoon%28+%283Y%5E4n%5E6%29%5E2%2F%28Y%5E2n%5E-3%29%5E4+%29
    For tutors: simplify_cartoon( (3Y^4n^6)^2/(Y^2n^-3)^4 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at %283%2AY%5E4%2An%5E6%29%5E2%2F%28Y%5E2%2Ahighlight_red%28+n%5E-3+%29%29%5E4.
Negative power changes multiplication to division
It becomes %283%2AY%5E4%2An%5E6%29%5E2%2F%28Y%5E2%2Fhighlight_green%28+n%5E3+%29%29%5E4.
Look at .
Canceled out common factors (Y-(0)),(Y-(0))
Look at highlight_red%28+%28highlight_red%28+3%2AY%5E2+%29%29%2F%281%29+%29.
Remove unneeded parentheses around factor highlight_red%28+3+%29,highlight_red%28+Y%5E2+%29
It becomes highlight_green%28+3+%29%2Ahighlight_green%28+Y%5E2+%29%2F%281%29.
Look at highlight_red%28+3%2AY%5E2%2F%28highlight_red%28+1+%29%29+%29.
Remove unneeded parentheses around factor highlight_red%28+1%2F1+%29
It becomes 3%2AY%5E2%2Fhighlight_green%28+1+%29.
Look at 3%2AY%5E2%2Fhighlight_red%28+1+%29.
Remove extraneous '1' from product highlight_red%28+1%2F1+%29
It becomes 3%2AY%5E2.
Result: 3%2AY%5E2

Universal Simplifier and Solver


Done!

Answer by richwmiller(17219) About Me  (Show Source):