SOLUTION: i have to simplify this 1/8(3x+1)^(3/2) + 1/4(3x+1)^(1/2) ^ means to the power of if you didnt know

Algebra ->  Square-cubic-other-roots -> SOLUTION: i have to simplify this 1/8(3x+1)^(3/2) + 1/4(3x+1)^(1/2) ^ means to the power of if you didnt know      Log On


   

Question 132660: i have to simplify this
1/8(3x+1)^(3/2) + 1/4(3x+1)^(1/2)
^ means to the power of if you didnt know
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%281%2F8%29%283x%2B1%29%5E%283%2F2%29+%2B+%281%2F4%29%283x%2B1%29%5E%281%2F2%29+ Start with the given expression


%281%2F8%29%283x%2B1%29%5E%283%2A%281%2F2%29%29+%2B+%281%2F4%29%283x%2B1%29%5E%281%2F2%29+ Rewrite 3%2F2 as 3%2A%281%2F2%29


%281%2F8%29%28%283x%2B1%29%5E%281%2F2%29%29%5E3+%2B+%281%2F4%29%283x%2B1%29%5E%281%2F2%29+ Rewrite the first expression using the identity x%5E%28y%2Az%29=%28x%5Ey%29%5Ez


%281%2F8%29%28sqrt%283x%2B1%29%29%5E3+%2B+%281%2F4%29sqrt%283x%2B1%29+ Now rewrite %283x%2B1%29%5E%281%2F2%29 as sqrt%283x%2B1%29



Let u=sqrt%283x%2B1%29


%281%2F8%29u%5E3+%2B+%281%2F4%29u+ Plug in u=%283x%2B1%29%5E%281%2F2%29


%281%2F4%29u%28%281%2F2%29u%5E2+%2B+1%29+ Factor out the GCF %281%2F4%29u


%281%2F4%29%28sqrt%283x%2B1%29%29%28%281%2F2%29%28sqrt%283x%2B1%29%29%5E2+%2B+1%29+ Now substitute sqrt%283x%2B1%29 back in for u


%281%2F4%29%28sqrt%283x%2B1%29%29%28%281%2F2%29%283x%2B1%29+%2B+1%29+ Square sqrt%283x%2B1%29 to get 3x%2B1


%281%2F4%29%28sqrt%283x%2B1%29%29%28%281%2F2%293x%2B1%2F2+%2B+1%29+ Distribute


%281%2F4%29%28sqrt%283x%2B1%29%29%28%281%2F2%293x%2B3%2F2%29+ Combine like terms


sqrt%283x%2B1%29%281%2F4%29%28%281%2F2%293x%2B3%2F2%29+ Rearrange the terms


sqrt%283x%2B1%29%28%281%2F8%293x%2B3%2F8%29+ Distribute


%28%281%2F8%293x%2B3%2F8%29sqrt%283x%2B1%29+ Rearrange the terms