Question

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

Answer 1

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

Answer 2

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.

Answer 3

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

Answer 4

K, hold on. Going to read them

Answer 5

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 \[(a^m)^n=a^{mn}\]
\[a^{-1}=1/a\]
\[a^{-2}=1/a^2\]

Answer 6

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

Answer 7

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.
\[(3ab^2)^3 = (3^3a^3b^6)^3\]

Answer 8

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

Answer 9

but you should get the idea

Answer 10

Not really

Answer 11

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

Answer 12

Do you understand that?

Answer 13

No

Answer 14

Which bit do you not understand

Answer 15

The exponets

Answer 16

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

Answer 17

I don't understand any of it

Answer 18

Which bit is confusing you?

Answer 19

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

Answer 20

You got this Anonymous! I believe in you!

Answer 21

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.

Answer 22

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.

Answer 23

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

Answer 24

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

Answer 25

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

Answer 26

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

Answer 27

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'

Answer 28

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

Answer 29

Okay bone that's enough..

Answer 30

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.

Answer 31

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

Answer 32

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

Answer 33

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

Answer 34

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

Answer 35

Hey anonymous we could get Jhann?

Answer 36

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

Answer 37

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?

Answer 38

What would a^2 * a^5 be?

Answer 39

a^10?

Answer 40

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

Answer 41

@Luigi0210 I will if i can't get it

Answer 42

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

Answer 43

So a^7?

Answer 44

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

Answer 45

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

Answer 46

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.

Answer 47

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?

Answer 48

Don't forget a = a^1.

Answer 49

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

Answer 50

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

Answer 51

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.

Answer 52

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

Answer 53

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?

Answer 54

Yes

Answer 55

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

Answer 56

hello professor

Answer 57

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

Answer 58

hahaha

Answer 59

i will try