Question

3^5 / (-3)^7 ... I believe that makes the base 0, right? So then what happens with the exponents? Help please!

Answer 1

When dividing exponential expressions with the same base, you subtract the corresponding exponents.

Answer 2

So you first need to make sure that the bases are the same

Answer 3

Notice how

(-3)^7 = (-1*3)^7

(-3)^7 = (-1)^7*(3)^7

(-3)^7 = -(3)^7

Answer 4

But they aren't, so now I am confused what I do instead. This is just one part of the question

Answer 5

I need someone to step by step explain what they are doing when they move all these numbers around and such, because I am not undetstanding by just looking at it

Answer 6

So

3^5/(-3)^7

is the same as

3^5/( -(3)^7 )

which simplifies to

- 3^5/3^7

Answer 7

Do you see how I'm getting all this?

Answer 8

I'm not because it's just numbers, I need it explained in english word by word step by step because just analyzing it confuses me even more. I need to verbally know what im doing so i can talk myself through the question

Answer 9

alright

Answer 10

In going from (-3)^7 to (-1*3)^7, I'm factoring -3 into -1 times 3

Answer 11

So

(-3)^7 = (-1*3)^7

Answer 12

From there, I'm raising everything inside the parenthesis to the 7th power like so

(-3)^7 = (-1)^7*(3)^7

Answer 13

Why are you doing that, where is that -1 coming from, why did you move the -3 to positive exponent?

Answer 14

Because I want to extract out the 3 (since the first base is a 3)

Answer 15

but the second is a -3, so we can say

-3 = -1 times 3

Answer 16

so just mentally you thought of that? is there something that tells you to do that?

Answer 17

mentally I did (just because I've been doing this a while), but you can divide the first base (3) by the second base (-3) to get


3/(-3) = -1

So you need to factor out a negative one from the second number to get the first number

Answer 18

Let me explain the full question. It is long, and I'm just focussing ONE of four parts
so doing this will take all day it seens? i am not understanding

Answer 19

alright

Answer 20

okay so always divide first base by second base? and use that number always? if there are uneven anyway?

Answer 21

not counting if they are the same as that is a much simpler formula

Answer 22

well in this case, it works out evenly...but it won't always give you an integer

Answer 23

i wish i could actually speak to someone on the phone or something, typing is so hard to explain everything

Answer 24

i understand, but you're doing great...you just have to keep at it

Answer 25

you can take a screenshot of it to save typing

Answer 26

i am taking an online class and this is honestly the hardest thing of my life. hardest thing i have EVER done or lack there of i guess you ccan say since i cant do anything :/

Answer 27

I'm sure you're doing fine. You just have to take things one step at a time.

Answer 28

and don't be so hard on yourself, I'm sure you can do lots of things well

Answer 29

It is not letting me attach the picture. can we try to email? can i do that on this site?

Answer 30

hmm maybe you can post the pic on a 3rd party site (like photobucket) and link it in

Answer 31

i am trying

Answer 32

http://a2.sphotos.ak.fbcdn.net/hphotos-ak-snc7/394505_10152043452630624_648218901_n.jpg

Answer 33

as i said, it is just one part of the equation but i want to focus on just it so i dont get any more confused than i already am

Answer 34

ok I see it now, one sec

Answer 35

you agree that you can factor -3 into -1 times 3 right?

Answer 36

yes that makes sense

Answer 37

so why not factor -3 into -1 times 3

so in step 2, rewrite everything in step 1, but instead of writing -3, write -1 times 3

Answer 38

But I did step two, the second line. is that wrong?

Answer 39

then raise every factor to their corresponding exponent

Answer 40

no, it's not wrong

Answer 41

The main question is the top top line. secondf line is what i did

Answer 42

I'm just breaking it down further

Answer 43

I dont understand how you want me to do that with everything else around it. what am i doing?

Answer 44

let me draw it out, one second

Answer 45

We have the following problem

\[\Large \frac{\left( 3x^4y^5z^7\right )^{5}}{\left(-3x^3yz^4 \right )^{7}}\]

correct?

Answer 46

yes, that is the original question and i broke it down further and did one other step, the second line on the picture i sent you

Answer 47

and frokm what i understand, that was right. now you are talking to me about the third step and that is where i am getting vconfused

Answer 48

here's what I mean in step 2

Answer 49

\[\Large \frac{\left( 3x^4y^5z^7\right )^{5}}{\left(-3x^3yz^4 \right )^{7}}\]


\[\Large \frac{\left( 3x^4y^5z^7\right )^{5}}{\left(-1*3x^3yz^4 \right )^{7}}\]

Answer 50

step 3 is then...

Answer 51

so what you are saying isw that before i do anything else, i should try to get the bases the same, then go forth, right?

Answer 52

\[\Large \frac{\left( 3x^4y^5z^7\right )^{5}}{\left(-3x^3yz^4 \right )^{7}}\]


\[\Large \frac{\left( 3x^4y^5z^7\right )^{5}}{\left(-1*3x^3yz^4 \right )^{7}}\]


\[\Large \frac{\left( 3\right)^{5}\left(x^4\right)^{5}\left(y^5\right)^{5}\left(z^7\right )^{5}}{\left(-1\right )^{7}*\left(3\right )^{7}\left(x^3\right )^{7}\left(y\right )^{7}\left(z^4 \right )^{7}}\]

Answer 53

Do you see where to go from here?

Answer 54

So let me try to do this but it will be wrong i am assuming so can you help explain why it is wrong?

Answer 55

alright, go for it

Answer 56

let me ask you something first

Answer 57

whats that

Answer 58

should i just be solving each line as it's own not even acting as if the other exists right niow? until i break it down firther?

Answer 59

like 3 to the power of five is 243. is that what i should be doing?

Answer 60

that's a good way to do it, taking it one step at a time (and not focusing on the other steps) will simplify things greatly

Answer 61

you can have that off to the side

Answer 62

3^5 = 243

(-1)^7 = -1

etc etc

Answer 63

once you have all the pieces, you can put them together to form a complete step

Answer 64

i should leave that for now and simplify the other ones with the exponents in brackets and exponents out of brackets, right? before i do anything else

Answer 65

this will avoid generating a million steps

Answer 66

you can think of

\[\Large \left( 3\right)^{5}\]

as

\[\Large \left( 3^{1}\right)^{5}\]

Answer 67

since 3^1 = 3

Answer 68

so you can then multiply each outer exponent with the corresponding inner exponent (for each term)

Answer 69

k but what im sayign is that one is already simplifed to the next level i guess you could call it so i should make the other ones with just one exponent like it is, right? sorry i make no sense. i am the dumbest person ever

Answer 70

no you're not, don't even think that

Answer 71

yes that is what i am saying. i think. okay hang on

Answer 72

yes go ahead and do what you're describing and I'll tell you if you did it correctly or not

Answer 73

okay i have a feeling the bottom line is wrong but i did my best.

Answer 74

show me what you got

Answer 75

http://a7.sphotos.ak.fbcdn.net/hphotos-ak-ash4/488369_10152043559615624_302584141_n.jpg

Answer 76

alright, let me have a look

Answer 77

how did you get 3^42 ?

Answer 78

the 42 is wrong ... 49 instead? forgot how to count lol

Answer 79

or maybe just leave at 3^7?

Answer 80

Yes just 3^7 or 2187

Answer 81

Since 3^7 = 2187

Answer 82

okay now can you explain why so i remember? because it is confusing me

Answer 83

\[\Large (3)^7 = \left(3^1\right)^7\]

agreed?

Answer 84

okay see i feel we should keep it at the first step because i didnt know that wheni wads doing the rest of the equation

Answer 85

you mean keep it (3)^7 ?

Answer 86

well like it is not being timsed by sseven like all the rest, so i need to remember that or i will always screw it up you kinow?

Answer 87

ah i see what you mean

Answer 88

you just have to remember that there's a 1 up there (by default)

Answer 89

i cant explain it, thats not what i mean. i dont know how to say it

Answer 90

if there is no exponent

Answer 91

hmm alright, but just keep that in mind

Answer 92

i dont understand what you said. even more confusion. you dont have to help mne if this is too much for you

Answer 93

I'm sorry, I didn't mean to confuse you further

Answer 94

I just want to keep that 1 there so i know, because if not i am doing something i should not be doing it seems

Answer 95

alright

Answer 96

anyway, now that i have that step, with the number changed from 42 to a simple 7, i am trying to figure out what to do next

Answer 97

your next step is to divide and simplify

Answer 98

how do i divide like this? i dont really divide, i add right? or no, subtract actually