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Mastering Powers and Exponents for Mathematical Success

Explore powers and exponents, learn order of operations (BEDMAS), and practice evaluating expressions with powers. Follow the methods and rules provided for accurate calculations. Improve your math skills with practical examples and exercises. Assignment due next class on pages 111-112.

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Mastering Powers and Exponents for Mathematical Success

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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 8 = 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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