document.write( "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. \r
\n" ); document.write( "\n" ); document.write( "(27a^3b)^-1/3(9a^-2b^2)^-1/2\r
\n" ); document.write( "\n" ); document.write( "Can anyone please help me with this, and show me in detail to break it down to get the answer :)\r
\n" ); document.write( "\n" ); document.write( "Thanks \n" ); document.write( "

Algebra.Com's Answer #24200 by hellyeah(21) $\"\"$ $\"About$

You can put this solution on YOUR website!
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Solved by pluggable solver: SOLVE any equation

Your Result:

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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.

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DETAILED EXPLANATION

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Look at

.
Multiplied denominator integers
It becomes $\"%2827%2Aa%5E3%2Ab%29%5E-1%2Fhighlight_green%28+6+%29%2F%289%2Aa%5E-2%2Ab%5E2%29%5E-1\"$ .
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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 $\"%2827%2Aa%5E3%2Ab%29%5E-1%2F6%2F%289%2Fhighlight_green%28+a%5E2+%29%2Ab%5E2%29%5E-1\"$ .
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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 $\"1%2Fhighlight_green%28+%2827%2Aa%5E3%2Ab%29%5E1+%29%2F6%2F%289%2Fa%5E2%2Ab%5E2%29%5E-1\"$ .
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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 $\"1%2F%2827%2Aa%5E3%2Ab%29%5E1%2F6%2Ahighlight_green%28+%289%2Fa%5E2%2Ab%5E2%29%5E1+%29\"$ .
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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 $\"%289%2Fa%5E2%2Ab%5E2%29%5E1%2F%2827%2Aa%5E3%2Ab%29%5E1%2F6\"$ .
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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 $\"highlight_red%28+1+%29\"$
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Look at $\"%289%2Fa%5E2%2Ab%5E2%29%2F%2827%2Aa%5E3%2Ab%29%5Ehighlight_red%28+1+%29%2F6\"$ .
Removing power of one $\"highlight_red%28+1+%29\"$
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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

.
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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

.
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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 $\"highlight_green%28+1+%29%2Fa%5E2%2Ab%5E2%2Fhighlight_green%28+3+%29%2Fa%5E3%2Fb%2F6\"$ .
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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 $\"1%2Fa%5E2%2Ab%5E2%2Fhighlight_green%28+18+%29%2Fa%5E3%2Fb\"$ .
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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 $\"1%2Ahighlight_green%28+a%5E%28-2-3%29+%29%2Ab%5E2%2F18%2Fb\"$ .
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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 $\"1%2Aa%5E%28-2-3%29%2Ahighlight_green%28+b%5E%28-1%2B2%29+%29%2F18\"$ .
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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 $\"1%2Aa%5E%28-2-3%29%2Ab%5E%28-highlight_green%28+1+%29%2B2%29%2F18\"$ .
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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 $\"a%5E%28-2-3%29%2Ab%5E%28-1%2B2%29%2F18\"$ .
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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 $\"a%5E%28highlight_green%28+-5+%29%29%2Ab%5E%28-1%2B2%29%2F18\"$ .
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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 $\"a%5E%28-5%29%2Ab%5E%28highlight_green%28+1+%29%29%2F18\"$ .
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Look at $\"a%5E%28-5%29%2Ab%5Ehighlight_red%28+%281%29+%29%2F18\"$ .
Removing power of one $\"highlight_red%28+%281%29+%29\"$
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Look at $\"a%5E%28highlight_red%28+-5+%29%29%2Ab%2F18\"$ .
Removed extra sign in front of $\"-5\"$
It becomes $\"a%5E%28-highlight_green%28+5+%29%29%2Ab%2F18\"$ .
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Look at $\"highlight_red%28+a%5E%28-5%29+%29%2Ab%2F18\"$ .
Negative power changes multiplication to division
It becomes $\"1%2Fhighlight_green%28+a%5E5+%29%2Ab%2F18\"$ .
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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: $\"b%2Fa%5E5%2F18\"$
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Universal Simplifier and Solver

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Done!
b/a^5/18

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