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Real Numbers & Radicals

Basic Algebra & Polynomials

Linear Equations

Inequalities & Absolute Value

Rational Expressions 1

Rat'l. Exp. 2 - mult&div

Rat'l. Exp. 3 - add&subt

Exponents

Slope & Equations of Lines

Review&Test

 

jdsmathnotes

 


UNIT 1  : ALGEBRA PREP

 LESSON 8: LAWS OF EXPONENTS

 

Examples of Powers:

25 = 2 x 2 x 2 x 2 x 2 = 32;   (-3)3 = (-3) x (-3) x (-3) = -27;    2.72 = 2.7 x 2.7 = 7.29

 

A POWER  (am ) consists of two parts; the base “a” and the exponent “m”.

 

Review of Basic Exponent Laws:

 

Rule

Example

Explanation

am x an = am+n

32 x 35 = 37

Multiplication Rule - If the bases are the same, add the exponents

Division Rule - If the bases are the same, subtract the exponents

(am)n = amn

(32)3=36

Power Rule – When taking a power of a power, multiply the exponents

(ab)m = amam

(3 x 2)4 = 34 x 24

Power of a Product – Take each factor in the product to that power

Power of a Quotient – Take numerator and denominator to that power

 

 

Example 1:  Simplify.

          

 

Solutions:

                                              

 

 

Example 2:  Simplify.

                                       

 

Solutions:

 

 

 

Example 3:  Simplify each of the following:

                                           

 

Solutions:

 

                                      

 

 

Alternate solution for c):

 

 

 

Rational Exponents:

 

 

Review of Radicals and Roots:

Example 2:

Text Box: Key Idea:
To find the 5th root of 32, work backwards – what number taken to the exponent 5 will yield 32??  25 = 32 and hence  .
To find the 4th  root of 81, work backwards – what number taken to the exponent 4 will yield 81??   34 = 81 and hence   .
                                          

 

Text Box: Key Points:
·	For fractional exponents, the denominator “n” gives the index of the root
·	The numerator “m” gives the exponent.
·	If n is an odd number, then x can be any real number, positive or negative.
·	If n is even, then x must be positive if we are working in the real number system
·	 
           

 

 

 

 

 

 

 

 

 

 

 

Example 4:  Simplify

 

                                                                                          

 

Solutions:

                                                   

 

                                                         

 

 

Example 5:  Simplify

                                                                                            

Solutions:

 

                                                       

 

 

Example 6:  Simplify

                                                                          

 

Solutions:

   

 

 

 

 

 

 

                                                                                

 

 

     

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