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2-6

2-6. Exponents. Course 3. Warm Up. Problem of the Day. Lesson Presentation. 2-6. Exponents. Course 3. Warm Up Find the product. 1. 5 • 5 • 5 • 5. 625. 27. 2. 3 • 3 • 3. –343. 3. (–7) • (–7) • (–7). 4. 9 • 9. 81. 2-6. Exponents. Course 3. Problem of the Day

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2-6

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  1. 2-6 Exponents Course 3 Warm Up Problem of the Day Lesson Presentation

  2. 2-6 Exponents Course 3 Warm Up Find the product. 1. 5 • 5 • 5 • 5 625 27 2. 3 • 3 • 3 –343 3. (–7) • (–7) • (–7) 4. 9 • 9 81

  3. 2-6 Exponents Course 3 Problem of the Day What two positive integers when multiplied together also equal the sum of the same two numbers? 2 and 2

  4. 2-6 Exponents Course 3 Learn to evaluate expressions with exponents.

  5. 2-6 Exponents Course 3 Vocabulary power exponential form exponent base

  6. 2-6 Exponents Course 3 The term 27 is called a power. If a number is in exponential form, the exponent represents how many times the base is to be used as a factor. Exponent Base 7 2

  7. 2-6 Exponents 4 • 4 • 4 • 4 = 44 d•d•d•d•d = d5 Reading Math Read 44 as “4 to the 4th power.” Course 3 Additional Example 1A & 1B: Writing Exponents Write in exponential form. A. 4 • 4 • 4 • 4 Identify how many times 4 is a factor. B. d • d • d • d • d Identify how many times d is a factor.

  8. 2-6 Exponents Course 3 Additional Example 1C & 1D: Writing Exponents Write in exponential form. C. (–6) • (–6) • (–6) Identify how many times –6 is a factor. (–6) • (–6) • (–6) = (–6)3 D. 5 • 5 5 • 5 = 52 Identify how many times 5 is a factor.

  9. 2-6 Exponents x • x • x • x • x= x5 d•d•d = d3 Course 3 Try This: Example 1A & 1B Write in exponential form. A. x • x • x • x • x Identify how many times x is a factor. B. d • d • d Identify how many times d is a factor.

  10. 2-6 Exponents Course 3 Try This: Example 1C & 1D Write in exponential form. C. (–3) • (–3) • (–3) • (–3) Identify how many times –3 is a factor. (–3) • (–3) • (–3) • (–3) = (–3)4 D. 7 • 7 Identify how many times 7 is a factor. 7 • 7 = 72

  11. 2-6 Exponents A. 35 B. (–3)5 = (–3) • (–3) • (–3) • (–3) • (–3) (–3)5 Course 3 Additional Example 2A & 2B: Evaluating Powers Evaluate. Find the product of five 3’s. 35 = 3 • 3 • 3 • 3 • 3 = 243 Find the product of five –3’s. = –243 Helpful Hint Always use parentheses to raise a negative number to a power.

  12. 2-6 Exponents D. 28 = (–4) • (–4) • (–4) • (–4) (–4)4 C. (–4)4 Course 3 Additional Example 2C & 2D: Evaluating Powers Continued Evaluate. Find the product of four –4’s. = 256 Find the product of eight 2’s. 28 = 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 = 256

  13. 2-6 Exponents A. 74 B. (–9)3 = (–9) • (–9) • (–9) (–9)3 Course 3 Try This: Example 2A & 2B Evaluate. Find the product of four 7’s. 74 = 7 • 7 • 7 • 7 = 2401 Find the product of three –9’s. = –729

  14. 2-6 Exponents D. 97 = (–5) • (–5) (–5)2 C. (–5)2 Course 3 Try This: Example 2C & 2D Evaluate. Find the product of two –5’s. = 25 Find the product of seven 9’s. 97 = 9 • 9 • 9 • 9 • 9 • 9 • 9 = 4,782,969

  15. 2-6 Exponents Course 3 Additional Example 3: Simplifying Expressions Containing Powers Simplify (25 – 32) + 6(4). = (32 – 9) + 6(4) Evaluate the exponents. = (23) + 6(4) Subtract inside the parentheses. Multiply from left to right. = 23 + 24 Add from left to right. = 47

  16. 2-6 Exponents Course 3 Try This: Example 3 Simplify (32 – 82) + 2 • 3. = (9 – 64) + 2 • 3 Evaluate the exponents. = (–55) + 2 • 3 Subtract inside the parentheses. Multiply from left to right. = –55 + 6 = –49 Add from left to right.

  17. 2-6 Exponents 1 2 1 2 1 2 1 2 1 2 1 2 (n2 – 3n) (72 – 3 • 7) (49 – 3 • 7) (49 – 21) (28) Course 3 Additional Example 4: Geometry Application Use the formula (n2 – 3n) to find the number of diagonals in a 7-sided figure. Substitute the number of sides for n. Evaluate the exponent. Multiply inside the parentheses. Subtract inside the parentheses. 14 diagonals Multiply

  18. 2-6 Exponents Course 3 Additional Example 4 Continued Verify your answer by sketching the diagonals. 14 Diagonals

  19. 2-6 Exponents 1 2 1 2 1 2 1 2 1 2 1 2 (n2 – 3n) (42 – 3 • 4) (16 – 3 • 4) (16 – 12) (4) Course 3 Try This: Example 4 Use the formula (n2 – 3n) to find the number of diagonals in a 4-sided figure. Substitute the number of sides for n. Evaluate the exponents. Multiply inside the parentheses. Subtract inside the parentheses. 2 diagonals Multiply

  20. 2-6 Exponents Course 3 Try This: Example 4 Continued Verify your answer by sketching the diagonals. 2 diagonals

  21. 2-6 Exponents n 4 Course 3 Lesson Quiz: Part 1 Write in exponential form. 1. n•n•n•n 2. (–8) • (–8) • (–8) (–8)3 3. Evaluate (–4)4 256 4. Simplify 99 – 3(4 • 23). 3

  22. 2-6 Exponents Course 3 Lesson Quiz: Part 2 5. A population of bacteria doubles in size every minute. The number of bacteria after 5 minutes is 15  25. How many are there after 5 minutes? 480

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