GCSE maths: negative and fractional powers

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!

Reply 1

ithinkitslily

16

hey, i get them quite well, do you have any examples that you've got stuck on?

Reply 2

_Xenon_

12

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?

Reply 3

Beth Mitchell

OP

7

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!

Reply 4

thefatone

6

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!

15^{\frac{2}{3}}, 215^{\frac{1}{3}}, 20^{\frac{3}{5}}

.... 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

Reply 5

Gerry-Atricks

22

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

Reply 6

Beth Mitchell

OP

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?

Reply 7

Beth Mitchell

OP

7

Thanks! I didn't see your message before I sent that one

Reply 8

Beth Mitchell

OP

7

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

Reply 9

Gerry-Atricks

22

Yes that is correct

Posted from TSR Mobile

Reply 10

ithinkitslily

16

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. x^1/2 = square root of x
x^1/3 = 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:

15^2/3= (15²)^1/3
so you can do 15²(225) and then cube root it (=6.08...)