Question

(3x^3)^2(2x)^3

Answer 1

Here's what I've got so far

Answer 2

\[(3x ^{3})^{2} (2x)^{3} \]
3*2 gives me
\[3x^{6} (2x) ^{3}\]

Answer 3

If I times 3&2 that gives me
6
Adding 6&3=9
So that gives me
6x^{9}

Answer 4

Rightt :)

Answer 5

But When I checked it to see if i was right
(i subsittuted something for the x
It didn't add up right

Answer 6

@uri Come backkkkkkk!

Answer 7

Great your back :D

Answer 8

Let me see

Answer 9

Did you put 6x^9?

Answer 10

Yep

Answer 11

Try putitng 6x^18

Answer 12

Still comes up different

Answer 13

@terenzreignz

Answer 14

What are we trying to do here?

Answer 15

Call in reinforcements! :P

Answer 16

Simplifying the original expression

Answer 17

Laws of Exponents

Answer 18

\[\LARGE (3x^3)^2(2x)^3\]

Answer 19

Hey how did you make that bigger? I was trying that but I couldn't make it readable!

Answer 20

off-topic sorry

Answer 21

\large
\Large
\LARGE
\huge
\Huge
^ varying degrees of size

Answer 22

thanks :D

Answer 23

anyways...

Answer 24

Back to the problem

Answer 25

<nods>
Yes, the laws of exponents...
Much like how multiplication distributes over addition,
exponentiation distributes over multiplication.
Let me show you what I mean:
\[\Large (ab)^m\]
You just raise all the factors to the exponent
Like this
\[\Large a^mb^m\]

Answer 26

With that in mind, you can now easily simplify this bit:
\[\LARGE (3x^3)^2\color{red}{(2x)^3}\]

Answer 27

So that equals

\LARGE 2 ^{3} * x^{3}

Answer 28

sorry about the formatting
2^3 *x^3

Answer 29

Yeah... you should enclose it in \[\Large \text{\[ <stuff>\]}\]

Answer 30

ah thanks

Answer 31

And yes, you are correct, now \[\Large 2^3 = \color{red}?\]

Answer 32

Hey math lesson and latex!

Answer 33

That would be 8

Answer 34

That's right. So that bit:
\[\LARGE (3x^3)^2\color{red}{(2x)^3}\]just becomes
\[\LARGE (3x^3)^2(\color{red}{8x^3})\]
correct?

Answer 35

Alrighty! That makes sense

Answer 36

Now, do the same to this part:
\[\LARGE \color{blue}{(3x^3)^2}(\color{}{8x^3})\]

Answer 37

OK So do I add the 3&2 first?

Answer 38

Consider \(\Large x^3\) as a single entity for now.
Just tell me what happens to that 2-exponent.

Answer 39

The 2 is added after \[3x^{3}]/ is solved

Answer 40

No, I mean, what happens here
\[\LARGE \color{blue}{(3x^3)^2}(\color{}{8x^3})\]

as per this rule:
\[\Large (ab)^m = a^mb^m\]

Answer 41

and it's \] at the end.

Answer 42

OH!
so that means 3^3*x^3

Answer 43

Why does 3 get cubed?
Was the exponent 3?

Answer 44

27^3?

Answer 45

And then I times 2*3

Answer 46

Time out

Answer 47

So that gives me
27^6

Answer 48

27^6 *8^3

Answer 49

Let's study this a little more closely, because your answers are (frankly) getting more and more outrageous...
\[\Large (3x^3)^2\]

Answer 50

Err sorry about that, this is a new topic for me

Answer 51

Understood, but this is one of the more basic, so I really don't want you to be having a hard time with this... because your speed at your more intermediate maths depends on whether or not this stuff is just second nature to you...so...

Answer 52

I understand!

Answer 53

Okay, so let's study this closely:
\[\Large (3x^3)^2\]
Now, I noticed you had no difficulty whatsoever in simplifying that other one
\[\Large (2x)^3=2^3x^3=8x^3 \]

Answer 54

Right the 3 is distributive inside the parenthesis.
Now that we have a exponent inside & outside the parenthesis, which do i solve first?

Answer 55

I'm glad you can identify your problem :)
Maybe, to get you started, we do a simple substitution.. just so you know, in a manner of speaking, where your priorities lie.

Let's let
\[\Large u = x^3\]
so that
\[\Large (3x^3)^2=(3u)^2\]
okay?

Answer 56

OK! So I have to solve the exponint inside the parenthisis first! next to the varible the expoint is closer to!

Answer 57

Or, here's what I think would be the easier way to look at things... Let's look at that example you handled so well:

Answer 58

OK

Answer 59

\[\Large (2x)^3\]

Answer 60

Right I distributed the 3 inside the parentheses

Answer 61

What the exponent outside actually does is MULTIPLY ITSELF to all the exponents inside the parenthesis.
Now, it's understood that when there's no exponent, that the exponent is 1...so...\[\Large (2^1x^1)^3\]

Answer 62

OK! So that's where the
x^2 came from!

Answer 63

So, 3 multiplies itself to all the EXPONENTS:
\[\Large 2^{1\times 3}x^{1\times3}= 2^3x^3 = 8x^3\]

Answer 64

Now, you can do likewise with
\[\LARGE (3x^3)^2\]Only this time, not all the exponents are 1.
No big deal, the same principle applies... go ahead now...

Answer 65

Just remember: The exponent *outside* the parentheses multiplies itself to each of the exponents *inside* the parentheses...

Answer 66

OK So that means
\[3^{1*2} & x ^{3*2}\]

Answer 67

Dang it

Answer 68

Never mind, it seems you got the correct idea :)

Answer 69

So that gives me

Answer 70

\[\Large 3^{1\times 2}x^{3\times 2}\]
simplify?

Answer 71

Thanks

Answer 72

OK so that gives me
3^2 * x^6

Answer 73

So that would give me
3x^8?

Answer 74

no... hold it

Answer 75

Correct up to this point:
\[\Large 3^2x^6\]
Now how on earth does this become
\[\Large 3x^8\]??

Answer 76

OH! I'm adding instead of multiplying
Should it become
3x^12?

Answer 77

No.

Answer 78

Hold on let me check the other equation

Answer 79

You don't move exponents around like that unless they have the same base!!!!

Answer 80

3 and x?
NOT the same base.

Answer 81

Oh never mind

Answer 82

Anyway, if we went by that logic, we should get
\[\Large 2^3x^3 = 2x^6 \] or something... clearly wrong

Answer 83

Right that's what I did

Answer 84

How did we simplify \[\Large 2^3x^3\]again?

Answer 85

We just added the two together and used the same exponint

Answer 86

So we got 2^3

Answer 87

2x^3

Answer 88

2^3 which is?

Answer 89

8

Answer 90

OH! OK! So 3^2 * x^6

Answer 91

Because 2^3 is jut a number.

Answer 92

And so is 3^2.

Answer 93

9x^6

Answer 94

yes.
(Really, before you should even think about doing algebra, make sure your grounding in Arithmetic is solid)

Answer 95

So ultimately, we get
\[\LARGE \color{blue}{(3x^3)^2}(\color{}{8x^3})=(\color{blue}{9x^6})(8x^3)\]

Answer 96

Yes I suppose I should have payed more attention in pre algebra

Answer 97

Thank you!

Answer 98

*Longest openstudy question for me to date*