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roger
Nov6-04, 09:56 AM
Hello,

please can someone help me with this :

Is 1 / (ab/d)^x/y the same as (d/ab) ^x/y ?

Does the order matter ?



Also, if I have to simplify root 10/root 160 and put it into surd form is 1/4
wrong ?


thanks


Roger

da_willem
Nov6-04, 10:02 AM
\frac{1}{(ab/d)^{x/y}}=(\frac{1}{(ab/d)})^{x/y}=(\frac{d}{ab})^{x/y}

So yes, it is the same

Also:

\frac{\sqrt{10}}{\sqrt{160}}=\sqrt{\frac{10}{160}} =\sqrt{\frac{1}{16}}=\frac{1}{4}

So you are again correct

arildno
Nov6-04, 10:02 AM
I assume you are talking about the expression:
\frac{1}{(\frac{ab}{d})^{\frac{x}{y}}}
By ordinary rules of arithmetic, we have:
\frac{1}{(\frac{ab}{d})^{\frac{x}{y}}}=\frac{(1)^{ \frac{x}{y}}}{(\frac{ab}{d})^{\frac{x}{y}}}=
(\frac{1}{\frac{ab}{d}})^{\frac{x}{y}}=(\frac{d}{a b})^{\frac{x}{y}}

Secondly, we have for positive, real numbers a,b:
\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}}
EDIT:
Hmm..dawillem beat me here..

roger
Nov6-04, 10:16 AM
I assume you are talking about the expression:
\frac{1}{(\frac{ab}{d})^{\frac{x}{y}}}
By ordinary rules of arithmetic, we have:
\frac{1}{(\frac{ab}{d})^{\frac{x}{y}}}=\frac{(1)^{ \frac{x}{y}}}{(\frac{ab}{d})^{\frac{x}{y}}}=
(\frac{1}{\frac{ab}{d}})^{\frac{x}{y}}=(\frac{d}{a b})^{\frac{x}{y}}

Secondly, we have for positive, real numbers a,b:
\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}}
EDIT:
Hmm..dawillem beat me here..

Dear Arildno,

The bit that says by the ordinary rules of arithmetic we have....

Why did you apply the x/y to the top and bottom ?
I thought it only applies to whats inside the brackets at the bottom ?
Please can you explain this for me



Also for the last bit, on roots, if it was root minus x / root minus y what is the general answer for that ?

Thanks


Roger

Zurtex
Nov6-04, 10:33 AM
Why did you apply the x/y to the top and bottom ?
I thought it only applies to whats inside the brackets at the bottom ?
Please can you explain this for me

It just made it easier and 1a=1 for any value of a.

CeeAnne
Nov6-04, 11:05 AM
Response to your first question: My understanding is the expressions are equivalent, as would be
1/((ab^x/y)/d^x/y) and (d^x/y)/(ab^xy). You need to observe any hierarchy is all.

The second is numerically correct. Unless you need to express it as root 1/16 or 1/root 16 for some reason.