SOLUTION: Multiply and simplify. Assume that all variables in a radicand represent positive real numbers. The 3 here is the cube root. 3√50x10γ * 3√25x16γ to the 7

Algebra ->  Radicals -> SOLUTION: Multiply and simplify. Assume that all variables in a radicand represent positive real numbers. The 3 here is the cube root. 3√50x10γ * 3√25x16γ to the 7      Log On


   

Question 29888: Multiply and simplify. Assume that all variables in a radicand represent positive real numbers. The 3 here is the cube root.
3√50x10γ * 3√25x16γ to the 7th power
Can you tell me how to get started.
Thanks so much!!!
Answer by Cintchr(481) About Me  (Show Source):
You can put this solution on YOUR website!
+%28root+%283%2C+50x10y%29+%2A+root%283%2C+25x16y%29%29%5E7+
I am assuming the whole thing here is to the 7th power, not just the second quantity. firstly .. since they are of the same root, and you are multiplying, you can bring everything under one root.
+%28root%283%2C+50x%2Ay%2A25x%2A16y%29%29%5E7+
prime factor all parts

rerite this so that all factors are grouped
+%28root%283%2C+%285%2A5%2A5%2A5%2A5%2A2%2A2%2A2%2A2%2A2%2A2%2Ax%2Ax%2Ay%2Ay%29%29%29%5E7+
since this is a cube root .... pull the factors out in groups of 3.

pull the 5, 2 and 2 out and multiply them
+%2820+%28root%28+3%2C+%285%2A5%2Ax%2Ax%2Ay%2Ay%29%29%29%29%5E7+
combine term within the root
+%2820+%28root%28+3%2C+%2825x%5E2y%5E2%29%29%29%29%5E7+
now taking it piece by piece ....
+20%5E7+=+128+
+%28root%28+3%2C+%2825x%5E2y%5E2%29%29%29%5E7+ look at the root and the power ....
3 goes into 7 twice with one left over ...
+%2825x%5E2y%5E2%29+%2825x%5E2y%5E2%29+%28root%28+3%2C+%2825x%5E2y%5E2%29%29%29+ multiply by the 128

+%2880000x%5E4y%5E4%29+%28root%28+3%2C+%2825x%5E2y%5E2%29%29%29+