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# Modulus related question watch

1. Hi,

I just wanted to ask if | x^3 + 8 | can be written as | x + 2 | ^3 ? or | x | ^3 + | 2 | ^3? (Is that the same thing )

I'm not too sure of the modulus properties but I do remember something about | x^n | = | x |^n or something like that. Can someone help me out thank you!
2. For your first question just think of a counter example to see you can't. Eg if x=1 then |1^3+8| is not equal to |1+2|^3, but you can write it as |x|^3+|2|^3Obviously the second modulus sign can be omitted as it is only a constant. So Yes you can write |x^n| as |x|^n. And |x+y| is never greater than the sum of its individule moduli ie |x|+|y|
3. (Original post by rockiee)
Hi,

I just wanted to ask if | x^3 + 8 | can be written as | x + 2 | ^3 ? or | x | ^3 + | 2 | ^3? (Is that the same thing )

I'm not too sure of the modulus properties but I do remember something about | x^n | = | x |^n or something like that. Can someone help me out thank you!
You can't split the modulus up.

If you're unsure then put in a simple case like x=1. |1^3+8|=9, using your proposed ideas: |1+2|^3=27 and |1|^3 +2 =3.
So you can see that they're not the same.

|x^n| = |x|^n. This only works if its the whole thing inside the modulus raised to the power n.
So in the example that you've given: x^3 +8 does not equal (x +2 )^3.
4. Oh...I get it now, thanks very much!
5. supposing that |x^n| = |x|^n... for x=-25 and n=1/2
|-25^1/2|=|sqrt-25| whereas |-25|^1/2=5...hence |x^n| = |x|^n is not true, surely?
6. (Original post by Esquire)
supposing that |x^n| = |x|^n... for x=-25 and n=1/2
|-25^1/2|=|sqrt-25| whereas |-25|^1/2=5...hence |x^n| = |x|^n is not true, surely?
It only applies when n is an integer.

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Updated: February 4, 2006
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