document.write( "Question 231372: Please explain how this would be worked out\r
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Algebra.Com's Answer #171259 by bamaboy(14)\"\" \"About 
You can put this solution on YOUR website!
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Solved by pluggable solver: SUBSTITUTION solver -- compute expression given values
Your Result:

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  • Graphical form: \"2a%5E-6b%5E2%2F18%2Fab%5E-5%2A%283b%29%5E-2\" simplifies to \"ab%5E5%2Fa%5E6%2F81\"
  • Text form: 2a^-6b^2/18/ab^-5*(3b)^-2 simplifies to ab^5/a^6/81
  • Cartoon (animation) form: \"simplify_cartoon%28+2a%5E-6b%5E2%2F18%2Fab%5E-5%2A%283b%29%5E-2+%29\"
    For tutors: simplify_cartoon( 2a^-6b^2/18/ab^-5*(3b)^-2 )
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  • If you have a website, here's a link to this solution.
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DETAILED EXPLANATION

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Look at .
Factors 2 and 18 have greatest common factor (GCF) of 2. Reducing fraction.
It becomes .
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Look at \"highlight_red%28+1+%29%2Aa%5E-6%2Ab%5E2%2F9%2Fab%5E-5%2A%283%2Ab%29%5E-2\".
Remove extraneous '1' from product \"highlight_red%28+1+%29\"
It becomes \"a%5E-6%2Ab%5E2%2F9%2Fab%5E-5%2A%283%2Ab%29%5E-2\".
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Look at \"highlight_red%28+a%5E-6+%29%2Ab%5E2%2F9%2Fab%5E-5%2A%283%2Ab%29%5E-2\".
Negative power changes multiplication to division
It becomes \"1%2Fhighlight_green%28+a%5E6+%29%2Ab%5E2%2F9%2Fab%5E-5%2A%283%2Ab%29%5E-2\".
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Look at \"1%2Fa%5E6%2Ab%5E2%2F9%2Fhighlight_red%28+ab%5E-5+%29%2A%283%2Ab%29%5E-2\".
Negative power changes multiplication to division
It becomes \"1%2Fa%5E6%2Ab%5E2%2F9%2Ahighlight_green%28+ab%5E5+%29%2A%283%2Ab%29%5E-2\".
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Look at \"1%2Fa%5E6%2Ab%5E2%2F9%2Aab%5E5%2Ahighlight_red%28+%283%2Ab%29%5E-2+%29\".
Negative power changes multiplication to division
It becomes \"1%2Fa%5E6%2Ab%5E2%2F9%2Aab%5E5%2Fhighlight_green%28+%283%2Ab%29%5E2+%29\".
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Look at \"highlight_red%28+1+%29%2Fa%5E6%2Ab%5E2%2F9%2Aab%5E5%2F%283%2Ab%29%5E2\".
Remove extraneous '1' from product \"highlight_red%28+1+%29\"
It becomes \"b%5E2%2Fa%5E6%2F9%2Aab%5E5%2F%283%2Ab%29%5E2\".
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Look at \"highlight_red%28+b%5E2+%29%2Fa%5E6%2F9%2Aab%5E5%2Fhighlight_red%28+%283%2Ab%29%5E2+%29\".
Canceled out common factors (b-(0)),(b-(0))
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Look at \"highlight_red%28+%28highlight_red%28+1+%29%29%2Fa%5E6%2F9%2Aab%5E5%2F%289%29+%29\".
Remove unneeded parentheses around factor \"highlight_red%28+1+%29\"
It becomes \"highlight_green%28+1+%29%2Fa%5E6%2F9%2Aab%5E5%2F%289%29\".
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Look at \"highlight_red%28+1%2Fa%5E6%2F9%2Aab%5E5%2F%28highlight_red%28+9+%29%29+%29\".
Remove unneeded parentheses around factor \"highlight_red%28+1%2F9+%29\"
It becomes \"1%2Fa%5E6%2F9%2Aab%5E5%2Fhighlight_green%28+9+%29\".
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Look at \"1%2Fa%5E6%2Fhighlight_red%28+9+%29%2Aab%5E5%2Fhighlight_red%28+9+%29\".
Multiplied denominator integers
It becomes \"1%2Fa%5E6%2Fhighlight_green%28+81+%29%2Aab%5E5\".
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Look at \"highlight_red%28+1+%29%2Fa%5E6%2F81%2Aab%5E5\".
Remove extraneous '1' from product \"highlight_red%28+1+%29\"
It becomes \"ab%5E5%2Fa%5E6%2F81\".
Result: \"ab%5E5%2Fa%5E6%2F81\"
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Universal Simplifier and Solver

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Done!
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