SOLUTION: What is {{{matrix(2,1,"", (6m)^(4/3)) }}} in radical form?

Algebra ->  Radicals -> SOLUTION: What is {{{matrix(2,1,"", (6m)^(4/3)) }}} in radical form?      Log On


   

Question 710080: What is
matrix%282%2C1%2C%22%22%2C+%286m%29%5E%284%2F3%29%29+
in radical form?
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Use the definition matrix%282%2C1%2C%22%22%2CB%5E%28A%2FC%29=root%28C%2CB%5EA%29+%29
matrix%282%2C1%2C%22%22%2CB%5E%28A%2FC%29=root%28C%2CB%5EA%29+%29
matrix%282%2C1%2C%22%22%2C%286m%29%5E%284%2F3%29=root%283%2C%286m%29%5E4%29+%29
Write the exponent 4 in terms of its nearest multiple of 3
less than 4, which is 3. So we write the exponent 4 as 3+1
matrix%282%2C1%2C%22%22%2C%286m%29%5E%284%2F3%29=root%283%2C%286m%29%5E%283%2B1%29%29+%29
Then write (6m)3+1 as (6m)3(6m)1
matrix%282%2C1%2C%22%22%2C%286m%29%5E%284%2F3%29=root%283%2C%286m%29%5E3%286m%29%5E1%29+%29
You can take out the cube root of (6m)3 as 6m in front of
the radical and you can erase the 1 exponent and the parentheses
under the radical and end up with:
matrix%282%2C1%2C%22%22%2C%286m%29%5E%284%2F3%29=6m%2Aroot%283%2C6m%29+%29
Edwin