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Laws of Exponents

First Law: If a is any real number and m, n are positive integers, there
 

 

 


 

Example : 



 

Example

Solve

Solution

 

Second Law: If a is any non-zero real number and m, n are positive integers, then



 

Example

Simplify

Solution



 

Example

Solution



 

 


Third Law : If a is any real number and m, n are positive integers, then

 

Example

Solve

Solution



 

Example

Evaluate

Solution



 

 

Fourth Law : If a, b are any real numbers and m is any positive integer then


 

Example

Simplify

Solution


 

Example

Simplify

Solution


Fifth Law: If a, b are real numbers and m is positive integer then

 

Example

Evaluate

Solution


 

Sixth law: If a is any real number then .

 

Example

 Find the value of

Solution


 

Example : Simplify


 

Example

Express as a power with the base 2.

Solution



 

Example

Simplify and write the answers in the exponential form

Solution

 

 

 



 

Example

Find m so that

Solution

 

Equating the exponents m + 10 = 9

m = 9 10 = 1



 

Example

Find the value of

Solution



 

Example

Find the value of

Solution

 





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