I was checking over my answers and saw one that looked like it could be simplified more. However, I am wondering if there is a reason why I stopped here. The directions say: Simplify. For informational purposes, I am using the glencoe meaning of simplifying, which is: it has no negative exponents, it has no fractional exponents in the denominator, it is not a complex fraction, and the index of any remaining radical is the least number possible.
The problem is: (3x + 4x^2) / x^(-2/3). Since x^-(2/3) has a negative exponent I put it in the numerator and get (3x+4x^2) * x^(2/3). Also, since we are supposed to put our exponents in descending order, I put the final answers as (4x^2 + 3x) * x^(2/3). I stopped here, because it seems to satisfy all the conditions of simplifying, but can't I multiply them? I might have just though ran out of time and when I came back to do it, I might have thought it was done and so went on to the next one.
The problem is: (3x + 4x^2) / x^(-2/3). Since x^-(2/3) has a negative exponent I put it in the numerator and get (3x+4x^2) * x^(2/3). Also, since we are supposed to put our exponents in descending order, I put the final answers as (4x^2 + 3x) * x^(2/3). I stopped here, because it seems to satisfy all the conditions of simplifying, but can't I multiply them? I might have just though ran out of time and when I came back to do it, I might have thought it was done and so went on to the next one.
