Chapter 7 linear equaTionS 185

EXAMPLES
Compute the following.

322 − () 4

This expression has three operations—multiplication, subtraction, and
exponentiation. According to PEMDAS, exponentiation is done first, so we
square 3 first.

322 −=() 49 − 24 ()

Multiplication follows exponentiation, so we multiply 2 and 4 next.

322 −=−=() 4924 () 98 −

Subtraction is performed last.

32 − 2(4) = 9 − 2(4) = 9 − 8 = 1

2(3 + 1)^2 = 2(4)^2 = 2(16) = 32

56 2
331

54

34

54

316

5

(^2212)
()
()
()
()
()
()
−

• ===
  4106
  10 35
  416
  10 15
  64
  25
  8
  5
  ()
  ()


• ()


• 
  

  =

  
  


• 
  

  ==
  In the next example, we will use the following root and exponent properties
  to simplify some of the expressions.
  aamn/ =n m ab= ab aa^2 =
  (^) [( 63 )]^23 −+ 82 /^2
  We begin by simplifying the expression inside the brackets.
  [( 63 )]^23 −+ 82 //^23 =−[() 69 82 +=](^2354 −+ 82 )//^23 = 48 2
  We now rewrite 483/2 as a root of a number raised to a power, and then we
  will simplify the root using the root properties above.
  [( 63 )]^23 −+ 82 //^23 =−[() 69 82 +=](^2354 −+ 82 )//^23 = 482
  = 448 48 48 48 48 48 48
  48 4348 16 3
  32 2
  2
  ==⋅=

  
  

  ()() ()
  ()() ()())(== 4843 ) 192 3
  EXAMPLES
  Compute the following.
  EXAMPLES
  Compute the following.