Question

How would you solve this. I need the necessary steps so I can understand. 2a(3a^2b)^2

Answer 1

WOLFRAM ALPHA

Answer 2

Solve or simplify? I'm not sure what you mean by solve

Answer 3

I am not for sure. Probably simplify

Answer 4

Ok..order of operations will require you to square what's inside the parenthesis first, which means you have to square the 3 and the a^2b. So you get 2a(9a^4b)...

Answer 5

then you multiply them and get 18a^(1+4b)

Answer 6

does it make sense?

Answer 7

would you square the the 3a first because of the square inside the parenthesis and square it again.

Answer 8

it depends, is it (3a)^2b or is it 3a^2b?

Answer 9

in the first case both the 3 and a are to be raised to the power of "2b" .. in the second case only the a will be

Answer 10

It is 2a (3a squared b)squared

Answer 11

so in that case, you don't want to square the 3 in the parenthesis twice. Let's look at just that part:

(3a^2b). Order of operations tells you that you must do your exponents first and then multiply. That means you must raise your a to the power of "2b" and then multiply by that 3.

Then you look outside of the parenthesis: (3a^2b)^2. So you have to square the entire thing in the parenthesis this time. So that's why you square your 3 as well and get (9a^4b). Then you look to the left: 2a(9a^4b) .. by the properties of exponents you get 18a^(1+4b) ... here your exponent becomes (1+4b) because of the "a" you multiplied by.

Answer 12

would it not be 2a (9a squared 2b)and then 2a(81a 2b) and then I am not for sure what comes next

Answer 13

Why do you say it should be (9asquared ^2b)? You only need distribute the 2b exponent through your "3" and "a^2b":

\[(3a^{2b})^2\]

So you have:
\[(9a^{4b})\]

Answer 14

if you have the expression 3a^2b.. which is what is inside your parenthesis.. you can't square your 3 because of order of operations. Once there are parenthesis around the whole expression .. like (3a^2b)^2 .. then you can take that exponent outside of the parenthesis and distribute it through

Answer 15

if inside your paranthesis there had been another set of parenthesis like: ((3a)^2b)^2 .. then you would be right

Answer 16

the expression is 2a(3a^2 b)^2
does this ^2 mean squared

Answer 17

yes... but first of all .. is the b part of your exponent?

Answer 18

No is not

Answer 19

and if you have 3a^2 .. that means 3 times a squared.. not (3a) squared

Answer 20

oh ok .. that wasn't clear from the expression... then it's still the same except you distribute the outside ^2 through your 3, "a^2b" and b. That means you get \[2a(9a^4b^2)\]

Answer 21

typo.. I meant to write 3, a^2 and b.. but the equation I wrote is correct

Answer 22

thank you so much for all the time you took to help me

Answer 23

no problem... make sure to multiply by the 2a in your final step to get 18a^4b^2

Answer 24

whoops again.. I meant 18a^5b^2

Answer 25

because of the a in 2a

Answer 26

The parenthesiswould it not be (81a b^2 ) then 2a (81a b^2) then (162^2b^2

Answer 27

Let me write out the expression in a clearer way and you can tell me if it's the one you're looking at

Answer 28

\[2a(3a^2b)^2\]

Answer 29

Like that right?

Answer 30

Yes but without the outside parenthsis \2a(3a^2b)^2\

Answer 31

hmm.. now I'm wondering what it is you actually see when I write that.. because it's kind of neat on my end.. look

Answer 32

This is what I originally saw \[2a(3a^2b)^2\]

Answer 33

like that.. because there are no outside parenthesis

Answer 34

does it come out like that on your end?

Answer 35

What are the out side marks then

Answer 36

I don't see any outside marks.. did you open that attachment I sent.. that's all I see

Answer 37

Yes just like that.

Answer 38

so then you see how it's only the a that's squared.. not the three.. inside the parenthesis.. right?

Answer 39

and then the parenthesis say "take this entire expression (3a^2b) and square it.. so you square each term 9 times a^4 times b^2

Answer 40

Ok this is new to me so I am still a little lost but this will help me as I progress isn this algebra.

Answer 41

Yes this is algebra.

Answer 42

Talk it out with a few other people if it helps. Maybe you'll understand their explanations better. Hope I helped some :) and all the best to you