SOLUTION: Please explain how this would be worked out Use only positive exponents in the answer 2a^-6b^2/18ab^-5*(3b)^-2

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Question 231372: Please explain how this would be worked out
Use only positive exponents in the answer
2a^-6b^2/18ab^-5*(3b)^-2
Answer by bamaboy(14) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SUBSTITUTION solver -- compute expression given values
Your Result:


YOUR ANSWER


  • 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 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at .
Factors 2 and 18 have greatest common factor (GCF) of 2. Reducing fraction.
It becomes .
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.
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.
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.
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.
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.
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))
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.
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.
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.
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

Universal Simplifier and Solver


Done!