Simplify x^0

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simplify \frac{x^{-3}y^{0}\cdot (xy^{-3})^{2}}{2x^{0}}

en

egiles wrote:

Hi,

for x<0,
|x-1| = 1-x
\(\sqrt{1-(x + 1) |x-1|}\)
=\(\sqrt{1-(x + 1)(1-x)}\)
=\(\sqrt{+x^2}\)
=\(\sqrt{x^2}\)
=|x|, again x<0
= -x

Answer (D)

Regards,

Hi!

I'm confused as why the answer isn't simply x (as opposed to-x). The absolute value of x, when simplified, is positive x, even if it is stated that x<0. Why do you go back and add a negative?

Thanks![/quote]



What is positive xwhen x is negative? What do you mean by absolute value of x, when simplified?
Is \(|-7| = -7?\) NOOOO! \(|-7|=-(-7)=7>0!!!\)
Absolute value is always non-negative.[/quote]


Hi EvaJager,

First, many thanks for the help you give me and others on this board. It is much appreciated.

Here is where my answer differed from yours. When I solved it, I reached this point:

= |x|
= x

Here is what you did:

= |x|
= -x

I am confused why you said the absolute value of x is -x. I thought all the absolute value of all numbers is non-negative.

Thanks again!
Eric[/quote]


I am asking the same question again: if \(x = -7,\) is \(|-7|=-7\)??? NO!!!
\(|-7| = 7\). But \(x\) is not \(7, \,\,x\) is \(\) What is the connection between \(-7\) and \(7?\)
Simply, \(7 = -(-7).\)
When \(x\) is negative, multiplying it by \(-1\) it turns it into a positive number. Therefore, \(|x|=-x\) for \(x<0.\)
You cannot write \(|-7|=\) A letter denoting a number if doesn't have a minus sign in front of it, it doesn't mean it cannot be negative. \(x\) doesn't automatically designate a positive number. You are stating yourself that \(x\) is negative!

Absolute value of a number expresses the distance on the number line between that number and 0. Distance between \(-7\) and \(0\) is \(7\).
A number \(x\) can be negative, for example \(x=-7\). And \(-x\) can be positive, if \(x=-5\), because \(-(-5)=5.\)