SOLUTION: I can't seem to figure this problem out. Need some serious help! I am suppose to simplify the radical square root 54xy^7 over square root 6xy. Assume that all variables represent

Algebra ->  Radicals -> SOLUTION: I can't seem to figure this problem out. Need some serious help! I am suppose to simplify the radical square root 54xy^7 over square root 6xy. Assume that all variables represent       Log On


   

Question 152334This question is from textbook Intermediate Algebra
: I can't seem to figure this problem out. Need some serious help!
I am suppose to simplify the radical square root 54xy^7 over square root 6xy. Assume that all variables represent positive numbers.
I appreciate anybody that can help me. This question is from textbook Intermediate Algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%2854xy%5E7%29%2Fsqrt%286xy%29 Start with the given expression.


sqrt%28%2854xy%5E7%29%2F%286xy%29%29 Combine the roots.


sqrt%289y%5E6%29 Divide %2854xy%5E7%29%2F%286xy%29 to get .


Convert from radical notation to exponent notation.


Rewrite as .


Multiply the outer exponent by each of the inner exponents.


Multiply the exponents.


sqrt%289%29y%5E3 Convert back to radical notation


3y%5E3 Take the square root of 9 to get 3


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Answer:

So sqrt%2854xy%5E7%29%2Fsqrt%286xy%29 simplifies to 3y%5E3


In other words, sqrt%2854xy%5E7%29%2Fsqrt%286xy%29=3y%5E3 where every variable is positive, x%3C%3E0, and y%3C%3E0