SOLUTION: 5y^3(y^5)^2 ___________ 10y^5(y^2)^6

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Question 118657: 5y^3(y^5)^2
___________
10y^5(y^2)^6
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%285y%5E3%28y%5E5%29%5E2%29%2F%2810y%5E5%28y%5E2%29%5E6%29 Start with the given expression


%285y%5E3y%5E%285%2A2%29%29%2F%2810y%5E5y%5E%282%2A6%29%29 Multiply the exponents



%285y%5E3y%5E10%29%2F%2810y%5E5y%5E12%29 Multiply


%285y%5E%283%2B10%29%29%2F%2810y%5E%285%2B12%29%29 Multiply the monomials by adding the exponents


%285y%5E13%29%2F%2810y%5E17%29 Add


5y%5E%2813-17%29%2F10 Now divide the monomials by subtracting the exponents



5y%5E%28-4%29%2F10 Subtract


y%5E%28-4%29%2F2 Now reduce 5%2F10 to get 1%2F2



1%2F2y%5E4 Now rewrite y%5E%28-4%29 as 1%2Fy%5E4


So %285y%5E3%28y%5E5%29%5E2%29%2F%2810y%5E5%28y%5E2%29%5E6%29 simplifies to 1%2F2y%5E4.


In other words, %285y%5E3%28y%5E5%29%5E2%29%2F%2810y%5E5%28y%5E2%29%5E6%29=1%2F2y%5E4