SOLUTION: Can someone please help me with this problem?? Simplify the expression; assume that all the variables represent positive numbers. (625x^4y)^1/4 ___________ __ (16xy^3)3/4 Th

Algebra ->  Expressions-with-variables -> SOLUTION: Can someone please help me with this problem?? Simplify the expression; assume that all the variables represent positive numbers. (625x^4y)^1/4 ___________ __ (16xy^3)3/4 Th      Log On


   

Question 105555This question is from textbook Intermediate Algebra
: Can someone please help me with this problem??
Simplify the expression; assume that all the variables represent positive numbers.
(625x^4y)^1/4
______________
(16xy^3)3/4
Thank You so much This question is from textbook Intermediate Algebra

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
%28625x%5E4y%29%5E%281%2F4%29%2F%2816xy%5E3%29%5E%283%2F4%29
Here are the useful exponent rules.
%28xyz%29%5ET=x%5ET%2Ay%5ET%2Az%5ET
x%5EM%2Ax%5EN=x%5E%28M%2BN%29
x%5EF%2Fx%5EG=x%5E%28F-G%29
%28x%5EP%29%5EQ=x%5E%28P%2AQ%29
Let's work on the numerator and denominator separately and then combine.
Numerator:
%28625x%5E4y%29%5E%281%2F4%29=625%5E%281%2F4%29%2Ax%5E%284%2A1%2F4%29%2Ay%5E%281%2F4%29Exponent rules from above.
%28625x%5E4y%29%5E%281%2F4%29=5%2Ax%5E%281%29%2Ay%5E%281%2F4%29Simplify.
%28625x%5E4y%29%5E%281%2F4%29=5xy%5E%281%2F4%29
Denominator:
%2816xy%5E3%29%5E%283%2F4%29=16%5E%283%2F4%29%2Ax%5E%283%2F4%29%2Ay%5E%283%2A3%2F4%29Exponent rules from above.
%2816xy%5E3%29%5E%283%2F4%29=8x%5E%283%2F4%29%2Ay%5E%289%2F4%29Simplfy.
Now let's combine them back together:

Exponent rules from above.
Simplify.
%28625x%5E4y%29%5E%281%2F4%29%2F%2816xy%5E3%29%5E%283%2F4%29=5x%5E%281%2F4%29%2F%288y%5E2%29Final answer.