math question?

Question

Okay, so I have these two probs. w/answers.
(I cant type root symbol ,the little thing that looks like a check mark)
cubed(3) root of 64Pcubed(3)=4P
and
fourth(4) root of 16P to the 4th power=2IPI
Why is the 2 lPl in absolute value and not the 4P???????

Answer 1

Even-index roots (square root, 4th root, etc.) of real numbers are by definition non-negative. Note that even if P is negative, 16 P^4 is positive so we can take its 4th root. However, that 4th root is not 2P, because that would be a negative number. So, an answer that gives a non-negative result, no matter what sign P has, is 2|P|.

Odd-index roots (cube root, 5th root, etc.) of real numbers do not have this restriction. The sign of the root is the same as the sign of the number whose root is being taken.

Answer 2

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