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# GCSE maths: negative and fractional powers

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1. This is probably one of the things I most get stuck on, and it tends to just be a really stupid mistake and I'll get them mixed up. If there's anyone who knows how to explain them and dumb them down a bit for me then that'd be great. Thanks!
2. hey, i get them quite well, do you have any examples that you've got stuck on?
3. (Original post by Beth Mitchell)
This is probably one of the things I most get stuck on, and it tends to just be a really stupid mistake and I'll get them mixed up. If there's anyone who knows how to explain them and dumb them down a bit for me then that'd be great. Thanks!
Sure I'll explain this for you...
Would you like me to choose an example?
4. Okay, so in a practice paper I've most recently got, it asks to order 15 to the power of 2/3, 215 to the power of 1/3 and 20 to the power of 3/5, I could probably do the ordering bit, its just knowing what to actually do, thanks btw!
5. (Original post by Beth Mitchell)
Okay, so in a practice paper I've most recently got, it asks to order 15 to the power of 2/3, 215 to the power of 1/3 and 20 to the power of 3/5, I could probably do the ordering bit, its just knowing what to actually do, thanks btw!

.... do you mean converting these into numbers without powers then ordering them?

in which case you root by the number on the bottom

then use the number at the top of the fraction as a power
6. how you approx do it:15^(2/3) equals the cube root of (15^2) approx 6.1
215^(1/3) equals the cube root of 215 which is just below 6
20^(3/5) equals the 5th root of (20^3) approx 6.03
7. so 15^2/3 would make cube root 15^2=6.08
215^1/3= cube root 215=5.99
20^3/5= 5 root 20^3= 6.03
Therefore 15^2/3 is the biggest?
8. Thanks! I didn't see your message before I sent that one
9. So am I right to assume as well that when it's a negative power, you do 1/the indice, to the power of whatever the power was
10. Yes that is correct

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11. when a number is to the power of -1, it means it is the reciprocal of the number
i.e. x-1 = 1/x

when a number is to the power of a fraction, it is the xth root of that number
i.e. x1/2 = square root of x
x1/3 = cube root of x

when you have a number to the power of, say, 2/3 or -1/3, you can make it more understandable by breaking it down, so:

152/3 = (152)1/3
so you can do 152 (225) and then cube root it (=6.08...)
12. (Original post by Beth Mitchell)
So am I right to assume as well that when it's a negative power, you do 1/the indice, to the power of whatever the power was
and .

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