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# Negative Exponents (negative indices)

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Today Ashlee asked me a non-specific question about how to handle negative indices.
i think this would be a common thing to have trouble with so i typed this up to help you.

If anyone has any queries or would llike me to show some more examples, just let me know.
When I was looking for this file I realized that i have posted many other similar ones for specific people lately.
sometimes surfing other peoples posts is a good idea.

140120 negative indices latex info.JPG
Jan 20, 2014

#4
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Hi Stu,

Stu:

a) How do I simplify 27^ -1x^ -1 / y^ -2?

27-1x-1 / y-2 = y2 / 27x

Please note:I used the 'sup' button above the smilies to write this.

b) What are rules for + - / * when you've a negative ^ -1 on a fraction bottom?
I am not sure what you mean but if the +- is not a part of the index you leave it alone.

c) As above when the ^ -1 is on top, is there time not to flip it or it cannot be flipped?
Well, they would all have to be factors in the numerator and the denominator.
for example
140206 neg indices.JPG

d) Does simplify have the ability to remove all negative powers in all equations?
Yes, I guess so - but it might be long and messy.

Feb 6, 2014
#5
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Thanks Melody,

"b) What are rules for + - / * when you've a negative ^ -1 on a fraction bottom?
I am not sure what you mean but if the +- is not a part of the index you leave it alone."

re: above I meant if we have an exponent of -1 in the below example,
eg. we simplify (-a^ -n)/ (b^ -n) = a^ m-n : to solve does m - -n ever become a +?

When does an odd amount of - and + exponents simplify an answer as - overall and an even amount of - and + or - and - simplify to +.
Does it apply to exponents or just applied to signs of coefficients and pronumerals? What about in division (top over bottom)?

Thanks.
Feb 6, 2014
#6
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Stu:

Thanks Melody,

"b) What are rules for + - / * when you've a negative ^ -1 on a fraction bottom?
I am not sure what you mean but if the +- is not a part of the index you leave it alone."

re: above I meant if we have an exponent of -1 in the below example,
eg. we simplify (-a^ -n)/ (b^ -n) = a^ m-n : to solve does m - -n ever become a +?
I think that you mean
-a-n / a-n => -a-n--n => -a-n+n => -a0 => -1
which was obvious really because the same thing was on the top and the bottom.
like -2/2 = -1 because the 2s cancelled out.

I just did this for someone else, maybe it will also help
140206 neg indices with fractions.JPG

When does an odd amount of - and + exponents simplify an answer as - overall and an even amount of - and + or - and - simplify to +.
Does it apply to exponents or just applied to signs of coefficients and pronumerals? What about in division (top over bottom)?

I don't know, you are making my head spin. (Sorry, I've been at this all day, I am not criticizing your efforts to absorb knowlege)
All the normal rules for minus signs apply. Are you sure you know them all.

Thanks.

Feb 6, 2014
#7
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bump
Feb 6, 2014
#8
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Learning, had 4 hours of maths study sessions and trying to put in the time. That's where I'm at and pushing along. Thanks.
Feb 6, 2014
#9
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I just did this for Stu so I thought I would tack it in here as well.

140208 more indices.JPG
Feb 7, 2014
#10
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140208 more indices (1).JPG
Please explain steps 4,5,6 to achieving 3a 5/3 to 9a10/6.

I don't see how to get to 10/6.
If so, I don't see difference of when we apply the exponent of a brack (in this instance to the power 2) before or after calculations. And have seen it done in both ways.

Firstly, 1/2 * 1/3 = 2/6 right? And if Squaring it = 2/6 * 2/1 then we can't rightfully square it again in step 5 which wouldn't = 10/6. And if we do square the exponent at step 5 how do you get to 10/6 the answer of 5/3 x 5/3 = 25/9. But I just don't see the links.
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Next -> 140120 negative indices latex info.JPG

I was shown to flip everything. I am pretty sure. In the questions I have been given to solve negative indices is as follows,
eg) 3/4 -2
=4 2/3 =12/3 =4 (confirmed in the answers.) So please outline what are the difference of application of what you told me and what I am shown.
-----------------------------------
Next -> 140206 neg indices (1).JPG

Ho do you go from division to multiplication. Has the equation been shifted around? I can't see it, except you're now got left over x 3 and right under y 2.

I guess I need to still know this flexibility of equations from / to * and + to - etc.
Feb 7, 2014
#11
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re: above, step 3 in last image. Where equal to 36 5/3, where do you get 5/3?

I'm reworking these same problems with the same issues.
Feb 8, 2014
#12
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Hi Stu,
I don't quite know where to start and i don't have a lot of time right now.
but
1/2 * 1/3 = (1*1)/(2*3) => 1/6
It is easier to see if the fractions are written upright.
When multiplying fractions multiply straight across the top, then multiply straight across the bottom.
A whole number can be written as a fraction by putting it over 1 so 3=3/1, 2x = (2x)/1 etc.

1/2 + 1/3 = 3/6 + 2/6 = 5/6
Again it is much better (but much more time consuming for me, in the forum) if you write the fractions upright.
Before you can add fractions you have to get a common denominator, preferably the lowest one.
The multiples of 2 are 2,4,6,8,
The multiples of 3 are 3,6,9,12,...
The lowest common one is 6.

Now, when you are getting rid of negative indices you only swap the thing with the negative indice to the other side of the fraction line. NOT everything.
3/4 -2 = 3 * 4 2 all over 1 if you like = 48
perhaps you are confusing it with
(3/4) -2 => (4/3) 2 => 16/9 => 1 and 7/9

Oh, dividing by a fraction.
When you divide by a fraction, you multiply by its reciprocal.
In other words, you turn the second one upside down and change the divide to a multiply.

You may need to work through some mathsisfun units on fractions I think Stu.
Anyway, I hope that this is a good start to helping you out.
Feb 8, 2014
#13
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Melody:

Hi Stu,
I don't quite know where to start and i don't have a lot of time right now.
but
1/2 * 1/3 = (1*1)/(2*3) => 1/6
It is easier to see if the fractions are written upright.
When multiplying fractions multiply straight across the top, then multiply straight across the bottom.
A whole number can be written as a fraction by putting it over 1 so 3=3/1, 2x = (2x)/1 etc.
>>>
^knew

1/2 + 1/3 = 3/6 + 2/6 = 5/6
Again it is much better (but much more time consuming for me, in the forum) if you write the fractions upright.
Before you can add fractions you have to get a common denominator, preferably the lowest one.
The multiples of 2 are 2,4,6,8,
The multiples of 3 are 3,6,9,12,...
The lowest common one is 6.
>>>>
in bold probably where i am making my errors which was oversight and from little maths exposure, even overlooking it in maths is fun/where it is to be applied.

Now, when you are getting rid of negative indices you only swap the thing with the negative indice to the other side of the fraction line. NOT everything.
3/4-2 = 3 * 42 all over 1 if you like = 48
perhaps you are confusing it with
(3/4)-2 => (4/3)2 => 16/9 => 1 and 7/9
>>>
Just working as shown by the nuclear physicist and correct according to answer sheet as a simplify. Maybe just a part of the entire process so you're right too is my guess.

Oh, dividing by a fraction.
When you divide by a fraction, you multiply by its reciprocal.
In other words, you turn the second one upside down and change the divide to a multiply.

^haven't had to apply, surely it can simplify some situations and I will need to learn.

You may need to work through some mathsisfun units on fractions I think Stu.
Anyway, I hope that this is a good start to helping you out.

Feb 8, 2014