SOLUTION: I have a homework problem i cant seem to figure out. I need to perform the operation, write the answer without negative exponents. Assume all variables represent positive numbers.

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Question 38644: I have a homework problem i cant seem to figure out. I need to perform the operation, write the answer without negative exponents. Assume all variables represent positive numbers.
(27a^3b)^-1/3(9a^-2b^2)^-1/2
Can anyone please help me with this, and show me in detail to break it down to get the answer :)
Thanks
Found 2 solutions by Nate, hellyeah:
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
%2827a%5E%283%29b%29%5E%28-1%2F3%29%289a%5E%28-2%29b%5E%282%29%29%5E%28-1%2F2%29
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1%2F%28%2827a%5E%283%29b%29%5E%281%2F3%29%289a%5E%28-2%29b%5E%282%29%29%5E%281%2F2%29%29
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1%2F%28%2827%5E%281%2F3%29%29%28a%5E%283%2A%281%2F3%29%29%29%28b%5E%281%2F3%29%29%289%5E%281%2F2%29%29%28a%5E%28-2%2A%281%2F2%29%29%29%28b%5E%282%2A%281%2F2%29%29%29%29
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1%2F%28%28%283%29ab%5E%281%2F3%29%29%28%283%29a%5E%28-1%29b%29%29
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1%2F%283ab%5E%281%2F3%293a%5E%28-1%29b%29
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a%2F%289ab%5E%284%2F3%29%29
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1%2F%289b%5E%284%2F3%29%29

Answer by hellyeah(21) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE any equation
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • Graphical form: %2827a%5E3b%29%5E-1%2F3%2F%289a%5E-2b%5E2%29%5E-1%2F2 simplifies to b%2Fa%5E5%2F18
  • Text form: (27a^3b)^-1/3/(9a^-2b^2)^-1/2 simplifies to b/a^5/18
  • Cartoon (animation) form: simplify_cartoon%28+%2827a%5E3b%29%5E-1%2F3%2F%289a%5E-2b%5E2%29%5E-1%2F2+%29
    For tutors: simplify_cartoon( (27a^3b)^-1/3/(9a^-2b^2)^-1/2 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at %2827%2Aa%5E3%2Ab%29%5E-1%2Fhighlight_red%28+3+%29%2F%289%2Aa%5E-2%2Ab%5E2%29%5E-1%2Fhighlight_red%28+2+%29.
Multiplied denominator integers
It becomes %2827%2Aa%5E3%2Ab%29%5E-1%2Fhighlight_green%28+6+%29%2F%289%2Aa%5E-2%2Ab%5E2%29%5E-1.
Look at %2827%2Aa%5E3%2Ab%29%5E-1%2F6%2F%289%2Ahighlight_red%28+a%5E-2+%29%2Ab%5E2%29%5E-1.
Negative power changes multiplication to division
It becomes %2827%2Aa%5E3%2Ab%29%5E-1%2F6%2F%289%2Fhighlight_green%28+a%5E2+%29%2Ab%5E2%29%5E-1.
Look at highlight_red%28+%2827%2Aa%5E3%2Ab%29%5E-1+%29%2F6%2F%289%2Fa%5E2%2Ab%5E2%29%5E-1.
Negative power changes multiplication to division
It becomes 1%2Fhighlight_green%28+%2827%2Aa%5E3%2Ab%29%5E1+%29%2F6%2F%289%2Fa%5E2%2Ab%5E2%29%5E-1.
Look at 1%2F%2827%2Aa%5E3%2Ab%29%5E1%2F6%2Fhighlight_red%28+%289%2Fa%5E2%2Ab%5E2%29%5E-1+%29.
Negative power changes multiplication to division
It becomes 1%2F%2827%2Aa%5E3%2Ab%29%5E1%2F6%2Ahighlight_green%28+%289%2Fa%5E2%2Ab%5E2%29%5E1+%29.
Look at highlight_red%28+1+%29%2F%2827%2Aa%5E3%2Ab%29%5E1%2F6%2A%289%2Fa%5E2%2Ab%5E2%29%5E1.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes %289%2Fa%5E2%2Ab%5E2%29%5E1%2F%2827%2Aa%5E3%2Ab%29%5E1%2F6.
Look at %289%2Fa%5E2%2Ab%5E2%29%5Ehighlight_red%28+1+%29%2F%2827%2Aa%5E3%2Ab%29%5E1%2F6.
Removing power of one highlight_red%28+1+%29
Look at %289%2Fa%5E2%2Ab%5E2%29%2F%2827%2Aa%5E3%2Ab%29%5Ehighlight_red%28+1+%29%2F6.
Removing power of one highlight_red%28+1+%29
Look at highlight_red%28+%28highlight_red%28+9%2Fa%5E2%2Ab%5E2+%29%29%2F%2827%2Aa%5E3%2Ab%29%2F6+%29.
Remove unneeded parentheses around factor highlight_red%28+9+%29,highlight_red%28+1%2Fa%5E2+%29,highlight_red%28+b%5E2+%29
It becomes highlight_green%28+9+%29%2Fhighlight_green%28+a%5E2+%29%2Ahighlight_green%28+b%5E2+%29%2F%2827%2Aa%5E3%2Ab%29%2F6.
Look at highlight_red%28+9%2Fa%5E2%2Ab%5E2%2F%28highlight_red%28+27%2Aa%5E3%2Ab+%29%29%2F6+%29.
Remove unneeded parentheses around factor highlight_red%28+1%2F27+%29,highlight_red%28+1%2Fa%5E3+%29,highlight_red%28+1%2Fb+%29
It becomes 9%2Fa%5E2%2Ab%5E2%2Fhighlight_green%28+27+%29%2Fhighlight_green%28+a%5E3+%29%2Fhighlight_green%28+b+%29%2F6.
Look at highlight_red%28+9+%29%2Fa%5E2%2Ab%5E2%2Fhighlight_red%28+27+%29%2Fa%5E3%2Fb%2F6.
Factors 9 and 27 have greatest common factor (GCF) of 9. Reducing fraction.
It becomes highlight_green%28+1+%29%2Fa%5E2%2Ab%5E2%2Fhighlight_green%28+3+%29%2Fa%5E3%2Fb%2F6.
Look at 1%2Fa%5E2%2Ab%5E2%2Fhighlight_red%28+3+%29%2Fa%5E3%2Fb%2Fhighlight_red%28+6+%29.
Multiplied denominator integers
It becomes 1%2Fa%5E2%2Ab%5E2%2Fhighlight_green%28+18+%29%2Fa%5E3%2Fb.
Look at 1%2Fhighlight_red%28+a%5E2+%29%2Ab%5E2%2F18%2Fhighlight_red%28+a%5E3+%29%2Fb.
Reduce similar several occurrences of highlight_red%28+1%2Fa%5E2+%29 to highlight_green%28+a%5E%28-2-3%29+%29
It becomes 1%2Ahighlight_green%28+a%5E%28-2-3%29+%29%2Ab%5E2%2F18%2Fb.
Look at 1%2Aa%5E%28-2-3%29%2Ahighlight_red%28+b%5E2+%29%2F18%2Fhighlight_red%28+b+%29.
Reduce similar several occurrences of highlight_red%28+b%5E2+%29 to highlight_green%28+b%5E%28-1%2B2%29+%29
It becomes 1%2Aa%5E%28-2-3%29%2Ahighlight_green%28+b%5E%28-1%2B2%29+%29%2F18.
Look at 1%2Aa%5E%28-2-3%29%2Ab%5E%28highlight_red%28+-1+%29%2B2%29%2F18.
Removed extra sign in front of -1
It becomes 1%2Aa%5E%28-2-3%29%2Ab%5E%28-highlight_green%28+1+%29%2B2%29%2F18.
Look at highlight_red%28+1+%29%2Aa%5E%28-2-3%29%2Ab%5E%28-1%2B2%29%2F18.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes a%5E%28-2-3%29%2Ab%5E%28-1%2B2%29%2F18.
Look at a%5E%28-highlight_red%28+2+%29-highlight_red%28+3+%29%29%2Ab%5E%28-1%2B2%29%2F18.
Added fractions or integers together
It becomes a%5E%28highlight_green%28+-5+%29%29%2Ab%5E%28-1%2B2%29%2F18.
Look at a%5E%28-5%29%2Ab%5E%28-highlight_red%28+1+%29%2Bhighlight_red%28+2+%29%29%2F18.
Added fractions or integers together
It becomes a%5E%28-5%29%2Ab%5E%28highlight_green%28+1+%29%29%2F18.
Look at a%5E%28-5%29%2Ab%5Ehighlight_red%28+%281%29+%29%2F18.
Removing power of one highlight_red%28+%281%29+%29
Look at a%5E%28highlight_red%28+-5+%29%29%2Ab%2F18.
Removed extra sign in front of -5
It becomes a%5E%28-highlight_green%28+5+%29%29%2Ab%2F18.
Look at highlight_red%28+a%5E%28-5%29+%29%2Ab%2F18.
Negative power changes multiplication to division
It becomes 1%2Fhighlight_green%28+a%5E5+%29%2Ab%2F18.
Look at highlight_red%28+1+%29%2Fa%5E5%2Ab%2F18.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes b%2Fa%5E5%2F18.
Result: b%2Fa%5E5%2F18

Universal Simplifier and Solver


Done!
b/a^5/18