Question

Can somebody Please give me the steps to do:
x^11y^3
---------
x^11y

Answer 1

So, when you divide like bases with exponents, do you add, subtract, multiply, or divide the exponents?

Answer 2

I've no clue.

Answer 3

Ok, what if you had \(x^4x^6\), what would that simplify to?

Answer 4

I think it would be x^10

Answer 5

That would be correct. What did you do?

Answer 6

I kept the base the same since X is the same as X and just added the exponents.

Answer 7

That is very good now, if you have \(\frac{x^6}{x^4}\), what would you do?

Answer 8

Im sorry, but I can't read what that says.

Answer 9

\[\frac{x^6}{x^4}\]

Answer 10

I would do xxxxxx
------
xxxx

Answer 11

and then cross out the x's that match so that I am left with two x's

Answer 12

COntinue

Answer 13

so then it would be x to the second?

Answer 14

***
I would do xxxxxx
------
xxxx
****

That is beautiful thinking. The last step is to notice the short cut. 6 x's up top
4 x's in the bottom. 6-4 = 2

Answer 15

Ok, now take a look at your original exponents, what would you do to get \[6 ? 4=2\]

Answer 16

6-4=2

Answer 17

So in general, if you have division of like bases you _______. If you have multiplication you _______.

Answer 18

If its division of like bases you keep them the same and if you have multiplication I dont know.

Answer 19

You just told me, that sentence is the same as \(x^4x^6\) and \[ {\frac{x^6}{x^4}}\]

Answer 20

oh I get it.

Answer 21

What did you do to the exponents

Answer 22

you just add the exponents and keep the bases the same if there already the same.

Answer 23

Technically that is correct for both, but For which were you implying? (might fall under semantics)

Answer 24

ok.

Answer 25

So which one do you add?

Answer 26

the exponents.

Answer 27

but for which function? (multiplication or division)

Answer 28

both

Answer 29

uhm, well depends on if you've learned something yet if that is correct

Answer 30

have you seen \[x^{-2}\]

Answer 31

can you re write that another way if you have?

Answer 32

yes, I think If I rewrite x^-2 It would be -x times -x

Answer 33

Ok, no that is not correct. So yes, normally when you have exponents, they are the short hand way of multiplying that many of the same number, but when you have a negative exponent it means '1 over" so ie.

Answer 34

\[x^n=x_1x_2....x_n\]\[x^{-n}=\frac{1}{x_1}\frac{1}{x_2}...\frac{1}{x_n}\]

Answer 35

Do you understand that^?

Answer 36

Not at all.

Answer 37

oh k uhm let me try and think of an easier way.... uh personally, I can't, so try and read this http://www.purplemath.com/modules/exponent.htm

Answer 38

this might be easier http://www.mathsisfun.com/algebra/exponent-laws.html,
but both are good

Answer 39

cannot find the file it says

Answer 40

which?

Answer 41

the mathisfun one.

Answer 42

oh delete the comma at the end

Answer 43

http://www.mathsisfun.com/algebra/exponent-laws.html

Answer 44

ok Thank you for all of the help. you are very smart.

Answer 45

You're trying to learn, that is all I can ask for.

Answer 46

Thank you, so once you read through that, we can go over this problem. Just come up with some ideas on how to simplify it, ok?

Answer 47

ok.

Answer 48

ok so my original problem was: x^11y^3
-------
x^11y

so putting that into scientific notation would be

xxxxxxxxxxx yyy
---------------
xxxxxxxxxxx y

wich would cancel out all the x's and leave it with just y^2
Is this correct?

Answer 49

That is, but can you do it without writing it all out?

Answer 50

No. I wasn't taught that there was another way do tell

Answer 51

Ok that second link shows it. They are called the basic laws/rules

Answer 52

so let m and n be any number

Answer 53

oh,cool.

Answer 54

ok

Answer 55

if you have \[x^mx^n=x^{m+n}\]
Do you follow?

Answer 56

I do.

Answer 57

ok now here is where that fraction \(\frac{1}{x^n}=x^{-n}\] comes into play

Answer 58

oops \[\frac{1}{x^n}=x^{-n}\]

Answer 59

If you have \[ x^m x^{-n}= \frac {x^m} {x^{n}}= x^{m-n}\]

Answer 60

ok, do you follow that

Answer 61

yes.

Answer 62

so now, you essentially have \[\frac{x^{11}}{x^{11}} \times \frac{y^3}{y}\]

Answer 63

Using the rules I just taught you, can you simplify this?

Answer 64

nope, I've got no clue. sorry eli5

Answer 65

...ok if I tell you that for x, m=11 AND n=11 can you figure it out then?

Answer 66

yup I think so, m multiplied by n and 11+11 ?

Answer 67

no, look at the eq please.

Answer 68

We have division

Answer 69

whats the eq?

Answer 70

I just don't understand it. Is it ok if I just write it out?

Answer 71

\[\frac{x^{11}}{x^{11}} \times \frac{y^3}{y}\]

Answer 72

Not really, you need to learn this. It will save you astronomical amounts of time

Answer 73

alright.

Answer 74

I shall learn.

Answer 75

ie \[x^{100}x^{200}\]

Answer 76

can you simplify that in less than 10 seconds?

Answer 77

x^300

Answer 78

ok, how did you do that?

Answer 79

I kept the bases the same since the both are x and then I added the exponents together.

Answer 80

good! now \[\frac{x^{200}}{x^{100}}\]

Answer 81

200-100=100, so x^100?

Answer 82

YES! now

Answer 83

yay

Answer 84

Now,
\[\frac{x^{11}}{x^{11}}\]

Answer 85

11-11=0 so x^0= just 1

Answer 86

YES! now \[\frac{y^3}{y}\]

Answer 87

3-0 ? if so then 3-0=3 so y^3

Answer 88

why is it 0?

Answer 89

As you just noted, anything to the zero power is 1

Answer 90

but anything to the _____ power is itself

Answer 91

oh so it's 3-1=2 so y^2

Answer 92

YUP!

Answer 93

Now, your eq. \[\frac{x^{11}}{x^{11}} \times \frac{y^3}{y}\]

Answer 94

Can you simplify this using this method?

Answer 95

11-11=0=1
3-1=2
so
1 times 2?

Answer 96

you forgot to keep your bases

Answer 97

oh yeah, woops.

X*Y^2 I think that would be it?

Answer 98

Stop you forgot something again