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## #1 2007-05-08 00:19:38

Toast
Real Member

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### Index Laws Practice

To complete these questions it will be necessary to know the Index Laws:
Law 1:

Law 2:

Law 3:

Law 4:

Law 5:

And the rational index laws:

Also, we define
, where

To prove this:
, but

1: Simplify with positive indices:
a)

b)

c)

d)

e)

2: Simplify with positive indices:
a)

b)

c)

d)

e)

3: Simplify with positive indices:
a)

b)

c)

d)

e)

4: Express as a power of x:
a)

b)

c)

d)

e)

Last edited by Toast (2007-05-08 00:22:15)

## #2 2007-09-24 22:57:56

nova_angel
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### Re: Index Laws Practice

Hey..thats cool...may you post some level 9 or secondary 3(asia) practice to the forum... i need more practise...anyway thank you~~this is kinda cool...

## #3 2007-12-29 17:58:29

kmlb123
Novice

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### Re: Index Laws Practice

ahhh...finally something i can understand ty for this stuff and could u upload some other stuff like medium level coordinate geometry (i drag at it)  TY4 THIS

## #4 2007-12-29 19:25:44

ganesh
Moderator

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### Re: Index Laws Practice

Hi kmlb123!
Happy to learn that you found this Exercise useful!
I shall post more exercises at Middle School/High School level;
certainly I shall try to post an exercise exclusively on Coordinate Geometry.

Character is who you are when no one is looking.

## #5 2013-01-08 16:38:53

Ash Okas
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### Re: Index Laws Practice

Exercise online, good see the stuff, helpful for kids and all, It inspired me to join the lovely forum, evoked my forgotten love for maths

## #6 2013-01-08 19:27:10

bob bundy
Moderator

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### Re: Index Laws Practice

hi

Some people discover this forum but don't realise there is a huge wealth of excellent math teaching material including exercises at

http://www.mathsisfun.com/

Try it!

Bob

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

## #7 2013-01-08 19:46:43

bobbym

Online

### Re: Index Laws Practice

Hi Ash Okas;

Welcome to the forum. Tell us about yourself in "Introductions."

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #8 2013-01-09 06:16:45

noelevans
Full Member

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### Re: Index Laws Practice

Hi Toast!    Nice set of problems!

Here is a variation of law 2 that is easy to use and always ends up with a non-negative exponent.
It takes care of all three cases:  m>n, m=n, m<n.  It is especially nice when the problem involves
negative exponents.

(p is the opposite of the smaller of m and n)  For example recalling that a^0 = 1 we get
( Whether this is true for a=0 has been thoroughly explored in other threads of this forum.)

m     n          p       a^(m+p)/a^(n+p)

2      5         -2     a^0 / a^3  = 1/(a^3)
3     -2          2     a^5 / a^0  =  a^5
-5     -3          5     a^0 / a^2  = 1/(a^2)
4     -7          7     a^11 / a^0 = a^11
3      3         -3     a^0 / a^0  = 1
-4     -4          4     a^0 / a^0  = 1

Of course the last two cases here would obviously be 1 from the start.

This law takes care of all cases for positive, negative or zero exponents m and n, leaving the
answer with a non-negative exponent for a in the numerator or denominator as most books