How does this algebra answer make sense???

Question

OK, so the question is to simplify (ab)^-3/2

 

My answer that I got is just 

 

  1

-----

√ab³

 

but the answer key says the right answer is 

 

√ab

-----

a²b²

 

Is this right and how do I get there???

Answer 1

Radicals are unacceptable (for various reasons: http://math.stackexchange.com/questions/26080/no-radical-in-the-denominator-why) in the denominator. It must be rationalized.

 

1 / √(ab)³                     multiply numerator and denominator by √(ab)

√(ab) / (√(ab)³(√(ab))  simplify

√(ab) / √(ab)⁴               take square root of denominator

√(ab) / (ab)²                 

√(ab) / a²b²

 

OK?