SOLUTION: i'm not understanding how to simplify radicals. The expression (cube root of 27x^2) times (cube root of 16x^4) is equivalent to

Algebra ->  Radicals -> SOLUTION: i'm not understanding how to simplify radicals. The expression (cube root of 27x^2) times (cube root of 16x^4) is equivalent to      Log On


   



Question 933784: i'm not understanding how to simplify radicals.
The expression (cube root of 27x^2) times (cube root of 16x^4) is equivalent to

Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The expression (cube root of 27x^2) times (cube root of 16x^4) is equivalent to
====
= cbrt[27x^2*16x^4]
----
= cbrt(3^3*2^3*x^6 *2]]
----
= 3*2*x^2 *cbrt(2)
----
= 6x^2*cbrt(2)
--------------------
Cheers,
Stan H.
---------------

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

root%283%2C27x%5E2%29%2A+root%283%2C16x%5E4%29..........use a root of product rule: root%28n%2Ca%29%2Aroot%28n%2Cb%29=root%28n%2Cab%29
root%283%2C27x%5E2%2A16x%5E4%29

root%283%2C27x%5E2%2A16x%5E4%29

root%283%2C27%2A16x%5E%282%2B4%29%29

root%283%2C27%2A16x%5E6%29....write 27 as 3%5E3,16 as 2%5E3%2A2,and x%5E6 as x%5E3%2Ax%5E3

root%283%2C3%5E3%2A2%5E3%2A2%2Ax%5E3%2Ax%5E3%29.....since root%283%2C3%5E3%29=3,root%283%2C2%5E3%29=2, and root%283%2Cx%5E3%29=x we have

3%2A2%2Ax%2Ax%2Aroot%283%2C2%29

6x%5E2%2Aroot%283%2C2%29