Simplify. -(3ab^2)^-3

- anonymous

Simplify. -(3ab^2)^-3

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- anonymous

\[-(3ab ^{2})^{-3}\]

- anonymous

http://www.mash.dept.shef.ac.uk/Resources/web-indicesandpowers.pdf
Make sure and learn every single rule on the first page of this document and you will never ask a similar question.

- anonymous

For this question you will need the second and the fifth rules

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## More answers

- anonymous

K, hold on. Going to read them

- anonymous

Tip: You can forget about the minus at the front and stick it on at the end, so you are working with (3ab^2)^-3
Use \[(a^m)^n=a^{mn}\]
\[a^{-1}=1/a\]
\[a^{-2}=1/a^2\]

- anonymous

okay I understand the fifth rule but not really the second one. So now we have \[(3ab ^{2})^{-3}\]

- anonymous

I will give you an example
\[(3ab^2)^3 = 3ab^2 * 3ab^2 * 3ab^2 = 27a^3b^6\]
or how you SHOULD approach this problem:
\[(3ab^2)^3 = (3^1a^1b^2)^3\] Now Multiply each power by 3.
\[(3ab^2)^3 = (3^3a^3b^6)^3\]

- anonymous

opes there shouldn't be brackets and power 3 at the end

- anonymous

but you should get the idea

- anonymous

Not really

- anonymous

What is confusing you? You multiply the powers of everything in the bracket by the main power outside the bracket.
\[(4ab)^4 = (4^1a^1b^1)^4 = 4^4a^4b^4\]

- anonymous

Do you understand that?

- anonymous

No

- anonymous

Which bit do you not understand

- anonymous

The exponets

- anonymous

Which bit exactly do you not understand? You multiply the exponents by the exponent outside the bracket:
\[(2ab^2)^2 = (2^1a^1b^2)^2 = 2^{1*2}a^{1*2}b^{2*2}=2^2a^2b^4\]

- anonymous

I don't understand any of it

- anonymous

Which bit is confusing you?

- anonymous

All of it. I have no clue how to do any of it.

- Luigi0210

You got this Anonymous! I believe in you!

- anonymous

I'm sorry but the only reason that you wouldn't understand what i've written out above is if you don't want to understand it. I suggest you change your attitude.

- anonymous

I told you already I don't understand the exponents, I read all your rules and comments and looked through my book before I even posted on here. I am just not good at math. I am doing my best I don't know why you think if you keep asking me the same question my answer will change.

- Luigi0210

And hey he is trying.. everyone learns at their own pace and has their own difficulties

- Luigi0210

And maybe you should try explaining it to him in a different sense :)

- anonymous

Thank you @Luigi0210 I don't understand why there are so many expomets like after every number

- anonymous

Like I really don't get where all these exponents are coming from

- anonymous

Oh, cry me a river. I've read so many people saying 'I am just not good at math' on this website it's just too funny to read. GUESS WHAT. No one is born a maths genius. The difference between you and me is not the knowledge but the believe that I CAN do it. If you sulk and just whine that you can't do any of it - you will keep sucking at maths. But if you man up and just open your eyes and try to understand the problem, you might find it clicking. You will never learn of succeed in ANY subject with an attitude of 'I'm no good at this'

- anonymous

Are you telling me that you can't do 1 times 2?

- Luigi0210

Okay bone that's enough..

- anonymous

Nope, no one is different. There are 3 groups of people, those who believe that they can do well in maths, those that don't and those who can't be arsed with anything at all. You are not getting a D+ in math because you are bad at maths, it is because you have a terrible 'i can't do it' attitude. And until you change it you will never succeed. And this goes for any subject not just maths. D+ at school math is shocking, school math is too easy not to get A's in it.

- anonymous

And it really does anger me especially with students who do well in other subjects.

- Luigi0210

Sorry if we are not all as perfect as you bone, just leave

- anonymous

Now that we've sorted this 'I can't do maths' nonsense, let's get back to the problem.

- anonymous

3 to the power of 3, to put this in english - it is 3 lots of 3's multiplied together.
So
3^1 - just 3
3^2 - 3 times 3 = 9
3^3 - 3 times 3 times 3 = 27
and this goes on. Do you understand this? If not please point to the word which you do not understand

- Luigi0210

Hey anonymous we could get Jhann?

- anonymous

I understand all of this and exponents in general just not how they're being used in the problem. I looked for a pattern before but they seemed kind of random to me

- anonymous

Okey. Now let's take a^2. Do you understand that this is a * a?
When you multiply numbers with the same base, you add the exponents together. So in this case a * a, the base is the same. It is a. So you just add the exponents, in this case the exponents are not written but they are by default - 1. Because a^1 = a. So you add two 1-s together and that is how you get a^2 from a * a. Do you understand that?

- anonymous

What would a^2 * a^5 be?

- anonymous

a^10?

- anonymous

When the base is the same, in this case it is a, you add the exponents

- anonymous

@Luigi0210 I will if i can't get it

- anonymous

In this case the exponents are 2 and 5. So what would it be?

- anonymous

So a^7?

- anonymous

Yes. This is the very first rule from the document i gave you http://www.mash.dept.shef.ac.uk/Resources/web-indicesandpowers.pdf
You said you don't understand it, well guess what, you just did.
When the base is the same, you can add the exponents together.
No let's take 3ab x a^7 = ? What would that be

- anonymous

This rule only goes for when you are multiplying don't forget that though

- anonymous

I read it but I didn't fully understand the n's and m's. it was easier to understand when you explained with the actual numbers.

- anonymous

Let's do the 3ab x a^7 example. Now in this case, you read this as 3 times a times b times a^7
Multiplication is COMMUTATIVE, that means it doesn't matter what order you chose to do the operations in. So you could do 3 times b times (a times a^7) Does this give you a clue to what the answer is?

- anonymous

Don't forget a = a^1.

- anonymous

If you don't understand something, point exactly to which word of sentense confuses you

- anonymous

Okay, Hold on I'm going to try working it out on paper again

- anonymous

We will take this step by step and we will get to the original problem. Trust me powers are easy and you WILL understand this.

- anonymous

Okay so back to the original problem \[-(3ab ^{2})^{-3}\]
you said to use \[(a ^{m})^{n} = a ^{mn}\] to solve, correct?

- anonymous

Yes. If the m and n is confusing you, let's change it to an example:
\[(a^3)^2=a^{3*2}\] is that better?

- anonymous

Yes

- anonymous

So do you understand what i mean by multiplication? Let's take another example.
\[(a^3b^4)^4\]
This is the same, but you have 2 things inside the bracket. The method does not change, you multiply the powers, first you do 3*4, that's how many a's you have and then 4*4, that's how many b's
\[a^{3*4}b^{4*4} = a^{12}b^{16}\]
Please point to something you don't get

- dan815

hello professor

- anonymous

I'm going to bed now, if she comes back please some how make her understand powers, it seems i am failing at my job :D

- dan815

hahaha

- dan815

i will try

- dan815

|dw:1370408774390:dw|

- Luigi0210

hey there dan :l

- dan815

hey

- dan815

whats up :D

- dan815

|dw:1370408868489:dw|

- Luigi0210

Just wondering.. hbu?

- dan815

|dw:1370408995976:dw|

- dan815

me nothing i was watching some tv show

- anonymous

Sorry I was checking on my bunny he was making a lot of noise and he keeps tipping his water over. I get him more water it's really hot here. Then my mom came to check on me, But I really need to get this done and more on in my assignment iy's getting super late

- anonymous

*had to get

- Luigi0210

It's hot here too D:
and what's your bunnies name?

- anonymous

Jack Ryan. It's the name of the main character in the first Bioshock.

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