fractions with negative exponents

**anthonye** · February 27th, 2011, 11:09 AM

Hi all;

I know how to solve fractions with negative exponents

but what happens when there's constant in the numereator
and/or the denominator.

Thanks.

**Archie Meade** · February 27th, 2011, 11:11 AM

If you post an example that you are stuck on,
it will be much easier to answer specifically.
Then the general cases will be much more obvious.

**anthonye** · February 27th, 2011, 11:17 AM

-15x^-1y^4z^-3 / 45x^-4yz^2 the answer is -x^3y^3 /3x^5

But what I want to know how to solve these type of fractions when there's a constant in the numerator and/or denominator.

**skeeter** · February 27th, 2011, 11:44 AM

Originally Posted by anthonye

-15x^-1y^4z^-3 / 45x^-4yz^2 the answer is -x^3y^3 /3x^5

But what I want to know how to solve these type of fractions when there's a constant in the numerator and/or denominator.

$\dfrac{-15x^{-1}y^4z^{-3}}{45x^{-4}yz^2} =$

$\dfrac{-15}{45} \cdot \dfrac{x^{-1}}{x^{-4}} \cdot \dfrac{y^4}{y} \cdot \dfrac{z^{-3}}{z^2} =$

$\dfrac{-1}{3} \cdot \dfrac{x^3}{1} \cdot \dfrac{y^3}{1} \cdot \dfrac{1}{z^5}$

**anthonye** · February 27th, 2011, 11:51 AM

Oops that should be 3z^5 in the denominator but how to solve if there was lets say
+whole any number or -whole any number in top or bottom of fraction.

**skeeter** · February 27th, 2011, 01:03 PM

Originally Posted by anthonye

Oops that should be 3z^5 in the denominator but how to solve if there was lets say
+whole any number or -whole any number in top or bottom of fraction.

why the confusion? just reduce the fraction if possible ...

$\dfrac{-15}{45} = \dfrac{-1}{3}$

... that's all.

**Archie Meade** · February 27th, 2011, 01:12 PM

Originally Posted by anthonye

-15x^-1y^4z^-3 / 45x^-4yz^2 the answer is -x^3y^3 /3z^5

But what I want to know how to solve these type of fractions when there's a constant in the numerator and/or denominator.

There is a constant in both the numerator and denominator in that example.
However, all terms in both the numerator and denominator are multiplied, so they are all factors.

Do you mean if you had terms combined by addition or subtraction instead of multiplication?
Then you try to factorise if possible.
If you are more specific,
someone can help you with an another example, if you post one.

**anthonye** · February 27th, 2011, 01:28 PM

Yes I do mean if the terms are combined with + - operators after the multiplication terms.

lets say I had +3 at the end.

**skeeter** · February 27th, 2011, 01:30 PM

Originally Posted by anthonye

Yes I do mean if the terms are combined with + - operators after the multiplication terms.

lets say I had +3 at the end.

post a relevant example ...

**anthonye** · February 27th, 2011, 01:47 PM

I havent got one to show you.

**Archie Meade** · February 27th, 2011, 01:54 PM

Ok then.

**anthonye** · February 27th, 2011, 01:58 PM

Just say at the end of the original numerator it had +3.

**Archie Meade** · February 27th, 2011, 02:02 PM

Originally Posted by anthonye

Just say at the end of the original numerator it had +3.

Yes, then you would split it into two fractions,
the original one and added to it we have 3 divided by the denominator,
which can be simplified as 45 is a multiple of 3.

Similar to (x+5)/10 = x/10 +5/10 = x/10 +1/2

**skeeter** · February 27th, 2011, 02:05 PM

Originally Posted by anthonye

Just say at the end of the original numerator it had +3.

$\dfrac{-15x^{-1}y^4z^{-3}+3}{45x^{-4}yz^2} =$

$\dfrac{-15x^{-1}y^4z^{-3}}{45x^{-4}yz^2} + \dfrac{3}{45x^{-4}yz^2} =$

$\dfrac{-x^3y^3}{3z^5} + \dfrac{x^4}{15yz^2}$

**anthonye** · February 27th, 2011, 02:13 PM

Yes of course you would just didn't think.

I'll have a better look tomorrow going to bed work in morning.

Thanks again.

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