There is an "art" into transcribing algebraic equations to one single line, as you have done.
I assume the original question in the book was NOT written on one line, but in fractional form, which explains why there are not parentheses.
The line in the middle of the fraction implies that the quantities above and below are to be calculated before the division.
When transcribing to a single line, numerators and denominators that exceed one single term should be enclosed in parentheses, for example:
4 x³ y-2
---------------------
2 x-1 y⁵
should be transcribed as:
(4 x³ y-2) / (2 x-1 y⁵)
to avoid ambiguity.
Most of the time, an expression like:
4x^3y^-2 / 2x^-1y^4
is assumed to be a fraction, but there is always a doubt, as in the present case.
If the assumption is correct, Gray's answer is correct.
The only way to confirm the answer is to confirm the question: was it written as a fraction with an expression above and below a line?
Hi Sorry I'm reposting this question, I think the answer that was provided was not correct because of the ambiguity of the original question but if I could have someone workout the question as written it would be much appreciated:
See below discussion.
4x^3y^-2 / 2x^-1y^4
is the answer:
2x^4y^-6 ?
Math - Gray, Saturday, November 20, 2010 at 4:51pm
((4x^3)(y^-2))/((2x^-1)(y^4) The way you typed your equation leaves some ambiguity; I'm assuming this is it. First move the variables with negative exponents to opposite sides of the fraction bar, and make those exponents positive. Then add the exponents and multiply the constants for each side. The answer is (8x^4)/(y^6).
Math - Tia, Saturday, November 20, 2010 at 5:45pm
The way I wrote it is exactly how the book has it. It's all written together without brackets. Very ambiguous I agree but I'm now not sure if the answer you provided is correct.
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