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Simplifying indices

1. Hi, I'm having trouble understanding how to do these.

e.g. 2^1/2 + 2^3/2
e.g. 4^1/3 - 4^4/3

I know that you need to factorise them, but am unsure how to
2. for the first, you take out a common factor - the highest power (in this case a fraction - don`t be put of) in both numbers - ie take out 2^(1/2) so you get 2^(1/2) x (1+2) - (because you`ll get the second factor being (2^(1/2))^2= 2^1=2) =3 x (sqrt 2).

2nd one - express the 4`s as powers of 2, then do similar...
3. (Original post by YLY)
Simplify 2^1/2 + 2^3/2 and 4^1/3 - 4^4/3
Okay... remember the following rule for indices.

Hence we may simplify indices using this rule.

My advice is similar to that which has been given, except I've used LaTeX to make things clearer.

I hope it helps.

Darren
4. Alternate route to the same answer is to think of 2^(3/2) as 2^(1+1/2) = 2^1 x 2^(1/2) - law of indices = 2 x root 2.

You can do the same for 4^(4/3).

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Updated: September 12, 2011
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