Simplify 3a · 3b ÷ 3c ÷ 3d. Help

- anonymous

Simplify 3a · 3b ÷ 3c ÷ 3d. Help

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- schrodinger

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- anonymous

Use dem parentheses.

- anonymous

As stated, your question is ambiguous.

- anonymous

the abc and d are exponents

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## More answers

- anonymous

if you do it from left to right

- anonymous

No, is it \(3b\div(3c\div3d)\) or \((3b\div3c)\div3d\)? These two are different things.

- anonymous

|dw:1371527789481:dw|

- anonymous

|dw:1371527864081:dw|

- anonymous

@timo86m That solution is not necessarily correct. We don't know the grouping.

- anonymous

dont need to if you just go from left to right.

- anonymous

That's not a safe assumption. I never did any left-to-right thing in college.

- anonymous

it is just order of operations
perenthesis. In this case non
exponents
multiplication and division from left to right

- anonymous

Citations, please. I don't see it anywhere in this.
http://en.wikipedia.org/wiki/Order_of_operations#The_standard_order_of_operations

- anonymous

it is always assumed left to right unless other wise stated by the perenthesis.

- anonymous

|dw:1371528260623:dw|

- anonymous

that is how i see the grouping anyhow.

- anonymous

So it's assumed that \(3^b\frac{1}{3^c}\frac{1}{3^d}\)?

- anonymous

http://www.wolframalpha.com/input/?i=3%5Ea+*3%5Eb+%C3%B7+3%5Ec%C3%B7+3%5Ed that is how wolfram sees it too.

- anonymous

Well, alright. I concede the point to you. But all this means is that whatever answer we give, there's a chance it's wrong because the original question was ambiguous.

- anonymous

|dw:1371528478926:dw|

- anonymous

draw it out @Scarr_Rose

- anonymous

3^a*3^b/3^c/3^d

- anonymous

draw it using the draw buttong silly :D

- anonymous

|dw:1371528774597:dw|

- anonymous

Oh my. Is that written exactly as you teacher gave it to you?

- anonymous

that is exactly how it looks in your book? If so then I am right :D

- anonymous

Or it could mean that the book is a really, really bad textbook.

- anonymous

|dw:1371528864889:dw|

- anonymous

That's still an ambiguity. Division is not commutative.
http://en.wikipedia.org/wiki/Division_ring

- anonymous

well thats just what my questions is asking.

- anonymous

I am right @scarr lol :D

- anonymous

its not a text book its online school. but thanks @timo86m

- anonymous

http://www.wolframalpha.com/input/?i=a%C3%B7b*c%3Da*c%C3%B7b @sledgehammer if you preserve the division sign then it is :D

- anonymous

"Similarly, there can be ambiguity in the use of the slash ('/') symbol in expressions such as 1/2x. If one rewrites this expression as 1 ÷ 2 × x and then interprets the division symbol as indicating multiplication by the reciprocal, this becomes..."
http://en.wikipedia.org/wiki/Order_of_operations#The_standard_order_of_operations

- anonymous

it isn't if
a ÷ b = b ÷ a not true
a*b ÷c = a ÷c * b is true
notice the sign is preserved :D meaning it applies to the c and only the c

- anonymous

The ambiguity can't be removed, because the question as stated doesn't actually work in mathematics. As I linked to you, division is not commutative. So writing it out like that is necessarily ambiguous.
WolframAlpha doesn't find it ambiguous because the syntax-reading grabs the next character only. It's like how TeX does it.

- anonymous

wolfram follows order of operations.

- anonymous

prove this statement wrong
a×b/c = a/c b
other than with c=0

- anonymous

Wolfram follows order of operations AND its own syntax. In other programming languages that only recognize strict order of operations, it will fail.
\[\frac bca=\frac a{cb}\\b^2=1\]

- anonymous

IN fact this is true too
a*b*c/d=a*b/d*c

- anonymous

No, it's not true, it's ambiguous. http://en.wikipedia.org/wiki/Division_ring

- anonymous

Dude I did not say a/(c*b) I said a/c b

- anonymous

That's why the original question should've included parentheses. Because you needed to write that out to make it clear.

- anonymous

You should've written (a/c)b and not a/c b, because the first has a precise meaning, and the second does not.

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