Powers and exponents

1
Weve got the power!

• Powers and exponents

Ya baby!
2
Order of operations

• you must follow the order of operations as
  follows
• Brackets
• Exponents
• Divide and multiply in the order that they appear
  left to right
• Add and subtract in the order that they appear
  from left to right

3
Determining the product of a power example 1

• How would you evaluate 3(2)³?
• Method 1 use repeated multiplication
• 3(2)³ 3 x 2³ 3 x 2 x 2 x 2 24
• Method 2 use order of operations
• 3(2)³ 3 x 16 24
• evaluate the exponent first

4
Determining the product of a power example 2

• How would you evaluate -3(-5)²?
• Method 1 use repeated multiplication
• -3(-5)² -3 x -5 x -5 -75
• Method 2 use order of operations
• -3(-5)² -3(25) -75

evaluate the exponent first
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Careful!!!!!

• Pay attention to the placement of the negative
  sign
• When it is in front of the whole expression,
  treat it as the coefficient -1
• Example -6² -1 x 6 x 6 -36
• Example (-6²) -1 x 6 x 6 -36
• When it is included within the brackets, and the
  exponent is outside the brackets, treat it as its
  own factor
• Example (-6)² -6 x -6 36

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Determining the product of a power Show me that
you know

• Complete these three practice questions using
  both methods
• 4 x 3² (one minute to solve before I show the
  responses)
• 4 x 3 x 3 36
• 4(9) 36
• 6(-2)³ (one minute to solve before I show the
  responses)
• 6 x -2 x -2 x -2 -48
• 6(-8) -48
• -7² (one minute to solve before I show the
  responses)
• -1 x 7 x 7 -49
• -(49) -49

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Evaluating expressions with powers

• Use the proper order of operations when
  evaluating expressions that contain powers!
• Example 1 4² - 8 2 (-3²)
• 16 8 2 (-9)
• 16 4 (-9)
• 12 (-9)
• 3

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Evaluating expressions with powers

• Example 2 -2 (-15 4²) 4(2 3)³
• -2 (-15 16) 4( 5)³
• -2 (-31) 4(125)
• 62 500
• 562

9
Evaluating expressions with powers Show me that
you know!

• Complete these two practice questions
• 4² (-4²) (one minute to solve before I show the
  response)
• 16 (-16)
• 0
• 8(52)² - 12 2² (1.5 minutes to solve before I
  show the response)
• 8(7)² - 12 2²
• 8(49) 12 4
• 392 3
• 389

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So what are the basic math truths???

• Expressions with exponents can have a numerical
  coefficient. Evaluate the exponent, then multiply
  by the coefficient
• Evaluate the expressions with powers using the
  proper order of operations (BEDMAS)

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Practice, practice, practice!

• Page 111 - 112
• Numbers 5, 6, 7, 8, 9

The assignment is due next class