SOLUTION: (25x^-1/2y^1/4)^1/2 This problem is out of Rational Exponents, Radicals, and Complex Numbers. This is not in a book but rather from my Algebra teacher. the -1/2 and 1/2 are ratio

Indicate the exponent of  as 
so that every factor has an exponent showing:


 
To remove the parentheses, multiply each of 
the three inner exponents by the outer 
exponent 





Put that over 1



Bring the factor  to the
bottom by changing the sign of the exponent:



Erase the 1 on the bottom:



Use the fact that  to rewrite 



Now we know that  so we replace that by 



Next write the  power as 
so that both fraction exponents will have the same
denominator:



Now use the fact that  to
rewrite the fractional powers as roots:



Rationalize the denominator by multiplying by 



Multiply under the radicals:



Simplfy the denominator as just , and write 
the numerator in alphabetical order:



and you can just put the 5 in the numerator and
eliminate the parentheses:



Edwin