Math Is Fun Forum

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Exponents

The exponent of a number says how many times to use the number in a multiplication.Exponent is also called power.

Last edited by Zeeshan 01 (2018-06-22 14:49:25)

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Malik

Bob

Administrator

Registered: 2010-06-20

Posts: 10,134

Re: Exponents

hi Zeeshan 01

What you are describing is called index notation.  It's just a way to show that a number is multiplied by itself many times without taking up loads of space.  eg:

and so on.

You may find this page helpful: http://www.mathsisfun.com/exponent.html

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Bob

Administrator

Registered: 2010-06-20

Posts: 10,134

Re: Exponents

So mathematicians invented index notation to apply to positive whole numbers like this

When y is multiplied by itself 'n' times:

This definition results in three laws of indices:

n and m are positive whole numbers (with n greater than m):

But mathematicians then wondered if there is a sensible way to extend the definition so that n and m can be any numbers.

If you specify that the three laws must still be obeyed then you can work out sensible definitions  for y^n when n is not a positive whole number.  For example, what about if n is zero?

using the first law.

So it is sensible to define y^0 to be 1 for all y.

Then if n is a negative whole number:

using the first law and what we have just learnt about a power of zero.

So define as follows:

This is now consistent with the first law as we have

You can continue like this is find sensible definitions for fractional powers and so on.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob