SOLUTION: (y^(3/4)/y^(-1/2))^8 I think the top number is x^6 and the bottom number is y^-4. How do I simplify that even more because you can't have a negative number.

Algebra ->  Exponents -> SOLUTION: (y^(3/4)/y^(-1/2))^8 I think the top number is x^6 and the bottom number is y^-4. How do I simplify that even more because you can't have a negative number.      Log On


   

Question 148092: (y^(3/4)/y^(-1/2))^8
I think the top number is x^6 and the bottom number is y^-4. How do I simplify that even more because you can't have a negative number.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If you have y%5E%28-1%2F2%29, you can rewrite this as y%5E%28-1%2F2%29=1%2Fy%5E%281%2F2%29.


If you have 1%2Fy%5E%28-1%2F2%29, you can rewrite this as 1%2Fy%5E%28-1%2F2%29=y%5E%281%2F2%29%2F1=y%5E%281%2F2%29.

So to rewrite a term with a positive exponent, simply flip the fraction.



%28y%5E%283%2F4%29%2Fy%5E%28-1%2F2%29%29%5E8 Start with the given expression.


%28y%5E%283%2F4%29y%5E%281%2F2%29%29%5E8 Flip the fraction 1%2Fy%5E%28-1%2F2%29 to get y%5E%281%2F2%29.


%28y%5E%283%2F4%2B1%2F2%29%29%5E8 When you multiply monomials with a common base, you simply add the exponents.



%28y%5E%285%2F4%29%29%5E8 Add the fractions.


y%5E%28%285%2F4%298%29 Multiply the inner and outer exponent.


y%5E%2840%2F4%29 Multiply.


y%5E%2810%29 Reduce.


So %28y%5E%283%2F4%29%2Fy%5E%28-1%2F2%29%29%5E8 simplifies to y%5E%2810%29


In other words, %28y%5E%283%2F4%29%2Fy%5E%28-1%2F2%29%29%5E8=y%5E%2810%29 where y%3E0