SOLUTION: the cubed root of 4x+1 to the 6th power

Algebra ->  Square-cubic-other-roots -> SOLUTION: the cubed root of 4x+1 to the 6th power      Log On


   



Question 397063: the cubed root of 4x+1 to the 6th power
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Is it
%28root%283%2C+4x%2B1%29%29%5E6
or
root%283%2C+%284x%2B1%29%5E6%29?
In this particular expression it ends up not making any difference. But in other situations it may make a big difference. So please use parentheses to make things clear. Use
"(the cubed root of 4x+1) to the 6th power" for the first one
and
"the cubed root of (4x+1 to the 6th power)" for the second one. Tutors are more likely to help if the problem is clear.

A quick way to simplify this expression takes advantage of fractional exponents. The general pattern for the relationship between radical expressions and expressions using fractional exponents is:
root%28a%2C+q%5Eb%29+=+%28root%28a%2C+q%29%29%5Eb+=+x%5E%28b%2Fa%29
As you can see, both %28root%283%2C+4x%2B1%29%29%5E6 and root%283%2C+%284x%2B1%29%5E6%29 are both equal to:
%284x%2B1%29%5E%286%2F3%29
The exponent simplifies to a 2:
%284x%2B1%29%5E2
And last of all we can use FOIL or the %28a%2Bb%29%5E2+=+a%5E2+%2B2ab+%2B+b%5E2 pattern to square 4x+1. (I like using the pattern.)
%284x%29%5E2+%2B+2%284x%29%281%29+%2B+%281%29%5E2
which simplifies to:
16x%5E2+%2B8x+%2B+1
This is the simplified result for both %28root%283%2C+4x%2B1%29%29%5E6 and root%283%2C+%284x%2B1%29%5E6%29.