Dividing by Monomials Paradox is $8x^2 \div 4x$ the same as $\frac{8x^2}{4x}$, which equals 2x, or we must use the order of operations such that $\frac{8x^2}{4} \times x$ which equals $2x^3$ 
 A: The spacing strongly supports the first interpretation (else it would be a deliberately misleading trick question). 

However, assuming the first interpretation was intended, the standard way to write the expression would be
$$\frac{8x^2}{4x}$$ 
which avoids misinterpretation since the fraction bar qualifies as a grouping symbol.

But if you wanted the latter interpretation, then, in order not to be misleading, each operation should be shown explicitly, as in
$$8 \times x^2 \div 4 \times x$$
or better, grouped, as in
$$\left(\left(8 \times x^2\right)\div 4\right) \times x$$
Finally, context should be considered. If the problem is from a chapter on order of operations, then I would choose the latter interpretation (i.e., strict order of operations). If it's from a chapter discussing adding, subtracting, multiplying, and dividing monomials, then, most likely, the former interpretation was intended (even though the author should have expressed it in fraction form). 

Also, as I suggested in one of my comments, assuming the problem is from a book, see if the author provides any worked examples with expressions of the given form.
