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)   (Show Source): You can put this solution on YOUR website!

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


YOUR ANSWER


  • Graphical form: simplifies to
  • Text form: (27a^3b)^-1/3/(9a^-2b^2)^-1/2 simplifies to b/a^5/18
  • Cartoon (animation) form:
    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 .
Multiplied denominator integers
It becomes .

Look at .
Negative power changes multiplication to division
It becomes .

Look at .
Negative power changes multiplication to division
It becomes .

Look at .
Negative power changes multiplication to division
It becomes .

Look at .
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes .

Look at .
Removing power of one highlight_red%28+1+%29

Look at .
Removing power of one highlight_red%28+1+%29

Look at .
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 .

Look at .
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 .

Look at .
Factors 9 and 27 have greatest common factor (GCF) of 9. Reducing fraction.
It becomes .

Look at .
Multiplied denominator integers
It becomes .

Look at .
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 .

Look at .
Reduce similar several occurrences of highlight_red%28+b%5E2+%29 to highlight_green%28+b%5E%28-1%2B2%29+%29
It becomes .

Look at .
Removed extra sign in front of -1
It becomes .

Look at .
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes .

Look at .
Added fractions or integers together
It becomes .

Look at .
Added fractions or integers together
It becomes .

Look at .
Removing power of one highlight_red%28+%281%29+%29

Look at .
Removed extra sign in front of -5
It becomes .

Look at .
Negative power changes multiplication to division
It becomes .

Look at .
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes .
Result:

Universal Simplifier and Solver


Done!
b/a^5/18

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