# Thread: fractions with negative exponents

1. ## fractions with negative exponents

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.

2. 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.

3. -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.

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

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

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

5. 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.

6. 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.

7. 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.

Then you try to factorise if possible.
If you are more specific,
someone can help you with an another example, if you post one.

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

lets say I had +3 at the end.

9. 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 ...

10. I havent got one to show you.

11. Ok then.

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

13. 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

14. Originally Posted by anthonye
Just say at the end of the original numerator it had +3.
$\dfrac{-15x^{-1}y^4z^{-3}+3}{45x^{-4}yz^2} =$

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

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

15. 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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