Simplify (8x^-2y^3)/4x^(1/2)y^-2

Question

I got the answer 2x^(5/2) y^5 but it was wrong.  The right answer is( 2y^5 radical x)/x^3

Answer 1

As I read it, your original numerator is 8x^-2y^{3 and}

the original denominator is 4x^½y^-2.

 

8/4 gives coefficient 2

Placing x squared in denominator to rid yourself of the negative exponent, and placing y squared in numerator for the same reason, you now will have

 

Numerator: 2y⁵

Denominator: x^5/2

 

To RATIONALIZE DENOMINATOR, multiply both top & bottom by an additional x^½ and you then get the correct answer.