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We’ve got the power!

We’ve got the power!. Powers and exponents. Ya baby!. 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.

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We’ve got the power!

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  1. We’ve 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

  5. 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

  6. 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

  7. 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

  8. 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(5+2)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

  10. 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)

  11. Practice, practice, practice! • Page 111 - 112 • Numbers 5, 6, 7, 8, 9 The assignment is due next class

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