Understanding Algebra

James W. Brennan
 

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Positive Integer Exponents

Meaning

32 = 3 × 3

 

33 = 3 × 3 × 3

 

In general xn = x · x · x · . . . · x (n factors of x)

 

x is the base, and n is the exponent (or power)

Rules

Product of Different Powers:    aman = am + n

  • IMPORTANT: all the numbers must have the same bases  (the same ‘a’)

Example:  (42)(43) = 45

 

This is easy to see if you write out the exponents:

 

(42)(43) = (4 · 4) · (4 · 4 · 4) = 4 · 4 · 4 · 4 · 4 = 45

 

 WARNING: Do not attempt to use this rule for addition:

 

42 + 43 is NOT 45. In fact there is no way to simplify xn + xm if n and m are different powers.

Power Raised to a Power:   

 

Example:  (42)3 = 46

 

This is also easy to see if you expand the exponents:

 

(42)3 = (42)(42)(42)

= (4 · 4) (4 · 4) (4 · 4)

= 4 · 4 · 4 · 4 · 4 · 4

= 46

 

There are more rules for combining numbers with exponents, but this is enough for now.

 
      

 


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James W. Brennan