struggle with early a level maths

Hi, I've decided to start doing Maths A Level again by myself and I'm going through the edexcel pure maths year 1 book and already struggling on very basic questions.

There are 2 questions that have stuck me. The first one was very simple of working out (-5)^-3. I worked this out originally as 1/-125, however the answer in the booklet says -1/125. This feels like an easy thing I should understand but yet I'm not.

I've got a question that asks to simplify 5x+3x^2 / 15x^3. I think I've done the first step correct in dividing both terms by the denominator and getting 5/15 * x^-2 + 3/15 * x^-1. However I don't know where to go from here. With 5/15 * x^-2, my belief was that to rid the minus in the power I would flip it to become 15 * x^2 / 5, with the x^2 being in the numerator. It's wrong and I can't work out why.

It's very worrying for me to struggle with these given it's so early in the content but I'm hoping these are fundamental issues I can fix and understand fully and have far less troubles going forward
Original post by 5udhafa
Hi, I've decided to start doing Maths A Level again by myself and I'm going through the edexcel pure maths year 1 book and already struggling on very basic questions.

There are 2 questions that have stuck me. The first one was very simple of working out (-5)^-3. I worked this out originally as 1/-125, however the answer in the booklet says -1/125. This feels like an easy thing I should understand but yet I'm not.

I've got a question that asks to simplify 5x+3x^2 / 15x^3. I think I've done the first step correct in dividing both terms by the denominator and getting 5/15 * x^-2 + 3/15 * x^-1. However I don't know where to go from here. With 5/15 * x^-2, my belief was that to rid the minus in the power I would flip it to become 15 * x^2 / 5, with the x^2 being in the numerator. It's wrong and I can't work out why.

It's very worrying for me to struggle with these given it's so early in the content but I'm hoping these are fundamental issues I can fix and understand fully and have far less troubles going forward

In maths, there are quite a few small things which can cause you to get a question "wrong" but actually youre nearly there. For
1/(-5)^3
then expanding you get 1/(-125) but its convention to put the negative sign on the numerator as 1/(-1) = -1/1 = -1 so it does equal -1/125.

For the second one, taking 5/15 x^(-2), the -2 exponent only applies to the x term so various equivalent ways of expressing this are
5/(15x^2) = 5/15 * 1/x^2 = 5/15 x^(-2) = 1/3 x^(-2) = 1/(3x^2) = 3^(-1) x^(-2)
(edited 2 months ago)