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Exponents - Lesson Summary

A number that represents how many times the number is multiplied by itself is known as exponent.

A given numbers can be expressed in standard as well as usual form.

Size of a plant cell = 0.00001275 m ← USUAL FORM

Standard Form
Any number expressed as a decimal number between 1.0 and 10.0, including 1.0 multiplied by a power of 10 is said to be in its Standard Form.

Standard Form= 1.275 x 10 -5m.

Negative integral exponent
 a -m =   1 a m    Where, m is a positive integer and a -m  is called the multiplicative inverse of a m .

Negative exponents can be used to express very small numbers.

Exponents to express small numbers in standard form
1) Take the number and see whether the number is between 1 and 10 or less than 1.

2) If the number is between 1 and 10 write it product of the number it self.

3) If the number is less than one then move the desimal point to the right so that there is just one digit on the left side of the desimal point.

4) Write the given number as the product of the number so obtained and 10-n, where n is the number of places where the desimal point has been moved to the right.

5) The number so obtained is the standard form.

For any non-zero integers a and b we have,

Laws of exponents

1. a m x a n = a m + n   
2. a m / a n = a m-n 
3. (a m) n = a mn  
4. a m x b m = (ab) m 
5. a m/b m = (a/b) m
6. a 0 = 1 .
Here m and n are integers.


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