**Algebra II, question 22, lesson 5**

We haven't started Algebra 2 yet, but in general, I think "simplify" just means "make it simpler" or sometimes "make it more useful - easier to use in a potential equation." Some things are pretty consistent, like combining all the "X" terms, or all of the known numbers. Another constant is probably reducing fractions to their lowest common denominator. But other things can vary with the particular number, such as whether you get rid of all parentheses (which is normally a good thing but sometimes a factored equation is going to be simpler / easier to use / match a factor in the numerator / etc.). Another variable might be deciding the best spot for the negative or the square root (normally it is better to have those on the top of a fraction, but it seems like occasionally that might complicate rather than simplify things?).8shininglights wrote:The question asks them to "simplify by adding like terms" (as in question 22, lesson 5).

The answer is written without fractions and with negative exponents.

My one daughter thought it was better to not have the negative exponent and put it in the denominator instead. I am wondering if this is actually "wrong." I know there are times where the directions will say to have your answer without negative exponents, so that is clear. But there have been a few problems in lesson 4, 5, and 6 where my child had the answer with a fraction and no negative exponents. Is there a rule that says one is more "simplified" than another way? (a fraction with no negative exponent vs. negative exponent and no fraction)

Lesson 6, #19 my child wrote 1/a5b3c (I don't know how to type exponents on here, so the 5 and 3 are exponents )

Lesson 5, #21 my child wrote -8m2p-7 (the 2 and -7 are exponents)

So, those two answers seem to contractict each other because in lesson 6 the answer key was with negative exponents, and lesson 5 they wanted that as a fraction. So, I am a bit confused! The instructions for both problems were "simplify." So.......is my daughter's answer actually wrong? Is there a rule to follow to know how they should be written. Thanks for taking the time to think this through with me!

That's my impression, anyways, and I give credit if the student has clearly made some changes and can defend their choices.

Julie