Question 960287: i have a question (-27)^5/3. Now i must bring this expression into radical form, if i can not then i must explain why not. My question is how do you know if it cant be put into radical form and does that mean if the answer is negative then its impossible or does it matter if it is.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! your expression is:
(-27)^(5/3)
this is the same as (the cube root of -27) raised to the third power, or the cube root of (-27 raised to the third power).
in algebra.com, cube root of x would be shown as root(3,x).
(-27)^(5/3) would be shown as root(3,x)^3 or as root(3,x^3)
both forms would get you the same answer.
you cannot take an even root of a negative number.
root(2,-27) is not allowed.
root(4,-27) is not allowed.
you can take an odd root of a negative number.
root(3,-27) is allowed.
root(5,j-27) is allowed.
the restriction on the even root because the solution is not real.
for example, what is the square root of -4?
the square root of 4 is either plus 2 or minus 2 because 2*2 = 4 and -2 * -2 is 4.
there is no real number that you can multiply by itself to get -4.
with the odd root, however, there is.
cube root of -27 is equal to -3 because -3 * -3 * -3 is equal to -27.
since you are dealing with the cube root, you can take the cube root of -27 and then raise it to the fifth power, or you can raise -3 to the fifth power and then take the cube root of it.
(-27)^(5/3) is equal to (-3)^5 which is equal to -243.
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