I would disagree with

Using PEMDAS/BODMAS/BEDMAS you have:

8÷2(1+3) =

8÷2(4) =

4(4) =

16

If we use an outdated way of dealing with this where everything on the left side of the divide sign is divided by the right side of the divide sign we have:

8÷2(1+3) =

8÷2(4) =

8÷8 =

1

This may be outdated, but is it really? I would say that it has nothing to do with everything on the left side being divided by the right, but exactly follows BODMAS i.e. what is in the brackets takes precedence and as you mentioned earlier the brackets are an implied multiplication.

I ought to have said "if ONE drops the brackets" rather than "if YOU drop the brackets" .The dropping of brackets idea came from a video

I watched.

For everyone who cited BODMAS or its equivalent and arrived at

8÷2(1+3) =

8÷2(4) =

Those that converted the brackets to a simple multiplication and followed the Left to Right rule must come up with the answer 16,

but is this interpretation a newer convention of the power of the brackets, or have they like politicians answered the question they wanted to answer, rather than the question they were asked?

Those that have retained the power of the brackets over both the division and left to right rule, must come up with the answer 1.

The maths teacher is this video.https://www.bing.com/videos/search?q=BODMAS&qpvt=BODMAS&view=detail&mid=2F1E0AD41CC31395E6BC2F1E0AD41CC31395E6BC&&FORM=VDRVRV

uses PEMDAS and a somewhat different convention where multiply comes before division in the acronym but are equivalent but obey the left to right rule. The question asked is 4 to the power 2-2 x( 8 ÷2) + 6 .

Notice the x sign before the brackets, which she drops after completing 8÷2, they are no longer needed because the required operation is clear, perhaps this is the new convention and brackets no longer mean retain the brackets and follow PEMDAS

Using her system of PEMDAS would seem to solve easily(?) your 2-4÷6+7 x 5+3÷17 x 5-3÷6÷12+3 = easily(?),

2-(4÷6)+(7 x 5)+[(3÷17) x{ 5-<(3÷6)÷12>}]+3 =

2-(24)+(35)+[0.18 x{ 5-<(0.5)÷12>}]+3 =

2-(24)+(35)+[0.18 x{ 5-0,42}]+3 =

2-24+35+[0.18 x 4.58]+3 =

2-24+35+0.82+3 =16.82 hopefully.

On further research on the problem.

It would seem that the BODMAS convention has been changed, and brackets are no longer required after completing the operation inside,

After dropping the brackets,you no longer have an operand to connect the rest of the equation, so I repeat that as originally written, the problem is unsolvable.

The only way round this is that after completing the contents, the brackets are an implied simple multiplication.or the addition of another operand is required to clarify what to do with the contents of the brackets.The modern answer would seem to be 16, and the older answer 1.