SOLUTION: Simplify {{{root(3,y^13)*root(3,81y^14)}}}

Algebra ->  Radicals -> SOLUTION: Simplify {{{root(3,y^13)*root(3,81y^14)}}}      Log On


   

Question 126389: Simplify

root%283%2Cy%5E13%29%2Aroot%283%2C81y%5E14%29
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
root%283%2Cy%5E13%29%2Aroot%283%2C81y%5E14%29 Start with the given expression


root%283%2Cy%5E13%2A81y%5E14%29 Combine the roots


root%283%2C81y%5E27%29 Multiply. Remember when you multiply like bases with exponents, you add the exponents.



Convert the expression from radical notation to exponent notation. Remember


Rewrite 81 as 81%5E1


Now distribute the exponent Now distribute the outer exponent 1%2F3 to each exponent in the parenthesis. Remember %28x%5Ey%29%5Ez=x%5E%28y%2Az%29

Now multiply the exponents

Reduce

Now convert back to radical notation

root%283%2C27%2A3%29y%5E9 Factor 81 into 27*3


root%283%2C27%29%2Aroot%283%2C3%29y%5E9 Break up the root


3%2Aroot%283%2C3%29y%5E9 Take the third root of 27 to get 3


3y%5E9%2Aroot%283%2C3%29 Multiply

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Answer:

So root%283%2Cy%5E13%29%2Aroot%283%2C81y%5E14%29 simplifies to 3y%5E9%2Aroot%283%2C3%29



In other words, root%283%2Cy%5E13%29%2Aroot%283%2C81y%5E14%29=3y%5E9%2Aroot%283%2C3%29