Negative Indicies Help (Year 10 Mathematics)

Can anyone please help me with negative indices? Basically I need to express them as positive indices but I seem to be struggling on doing the complicated ones. I understand the simple questions and know how to do them but the harder ones makes my brain go to a standstill.

Examples are

http://latex.codecogs.com/gif.latex?5x^-^2y^3/6xy^2 (I couldn't do the division sign so I replaced it with /)

http://latex.codecogs.com/gif.latex?\frac{4}{5}a^-^3

and lastly

http://latex.codecogs.com/gif.latex?...^5}{3a^-^2b^4}

Re: Negative Indicies Help (Year 10 Mathematics)

You need to apply $\displaystyle \displaystyle \begin{align*} a^{-n} = \frac{1}{a^n} \end{align*}$ to everything that has a negative index, then simplify any resulting fractions as much as you can. Try this, see how you go, if you need any more help please post what you have done and where you are stuck.

Re: Negative Indicies Help (Year 10 Mathematics)

5x^(-2)y^3/6xy^2

= 5x^(-2-1)y^(3-2)/6

= 5x^(-3)y^(1)/6

= 5y^(1)/6x^(+3)

= 5y/6x^3

4a^(-3)/5

= 4/5a^(+3)

= 4/5a^3

2m^3 n^(-5)/3a^(-2)b^4

= 2m^3 a^2/3n^(+5) b^4

= 2m^3 a^2/3n^5 b^4

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