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4-1. Exponents. Course 3. Warm Up. Problem of the Day. Lesson Presentation. 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. Problem of the Day

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  1. 4-1 Exponents Course 3 Warm Up Problem of the Day Lesson Presentation

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

  4. Learn to evaluate expressions with exponents.

  5. Vocabulary exponential form exponent base power

  6. If a number is in exponential form, the exponent represents how many times the base is to be used as a factor. A number produced by raising a base to an exponent is called a power. Both 27 and 33 represent the same power. Exponent Base 7 2

  7. 4 • 4 • 4 • 4 = 44 Reading Math Read –(63) as “-6 to the 3rd power or -6 cubed”. Additional Example 1: Writing Exponents Write in exponential form. A. 4 • 4 • 4 • 4 Identify how many times 4 is a factor. B. (–6) • (–6) • (–6) Identify how many times –6 is a factor. (–6) • (–6) • (–6) = (–6)3

  8. 5 • 5 = 52d4 Additional Example 1: Writing Exponents Write in exponential form. Identify how many times 5 and d are used as a factor. C. 5 • 5 • d • d • d • d

  9. x • x • x • x • x= x5 d•d•d = d3 Check It Out: Example 1 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. Check it Out: Example 1 Write in exponential form. C. 7 • 7 • b • b Identify how many times 7 and b are used as a factor. 7 • 7 = 72b2

  11. A. 35 B. (–3)5 = (–3) • (–3) • (–3) • (–3) • (–3) (–3)5 Additional Example 2: 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. D. 28 = (–4) • (–4) • (–4) • (–4) (–4)4 C. (–4)4 Additional Example 2: Evaluating Powers 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. A. 74 B. (–9)3 = (–9) • (–9) • (–9) (–9)3 Check It Out: Example 2 Evaluate. Find the product of four 7’s. 74 = 7 • 7 • 7 • 7 = 2401 Find the product of three –9’s. = –729

  14. D. 97 = –(5) • (5) –(5)2 C. –(5)2 Check It Out: Example 2 Evaluate. Find the product of two 5’s and then make the answer negative. = –25 Find the product of seven 9’s. 97 = 9 • 9 • 9 • 9 • 9 • 9 • 9 = 4,782,969

  15. y Evaluate x(yx – zy) + x for x = 4, y = 2, and z = 3. x(yx – zy) + x y Additional Example 3: Using the Order of Operations Substitute 4 for x, 2 for y, and 3 for z. = 4(24 – 32) + 42 = 4(16 – 9) + 16 Evaluate the exponent. Subtract inside the parentheses. = 4(7) + 16 Multiply from left to right. = 28 + 16 Add. = 44

  16. Evaluate z –7(2x – xy) for x = 5, y = 2, and z = 60. z – 7(2x – xy) Check It Out: Example 3 Substitute 5 for x, 2 for y, and 60 for z. = 60 – 7(25 – 52) = 60 – 7(32 – 25) Evaluate the exponent. = 60 – 7(7) Subtract inside the parentheses. = 60 – 49 Multiply from left to right. Subtract. = 11

  17. 1 2 1 2 1 2 1 2 1 2 1 2 (n2 – 3n) (72 – 3 • 7) (49 – 3 • 7) (49 – 21) (28) 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. Additional Example 4 Continued A 7-sided figure has 14 diagonals. You can verify your answer by sketching the diagonals.

  19. 1 2 1 2 1 2 1 2 1 2 1 2 (n2 – 3n) (42 – 3 • 4) (16 – 3 • 4) (16 – 12) (4) Check It Out: 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. Check It Out: Example 4 Continued A 4-sided figure has 2 diagonals. You can verify your answer by sketching the diagonals.

  21. 4 n Lesson Quiz: Part I Write in exponential form. 1. n•n•n•n 2. (–8) • (–8) • (–8)• (h) (–8)3h 256 3. Evaluate (–4)4 4. Evaluate x • z – yx for x = 5, y = 3, and z = 6. –213

  22. Lesson Quiz: Part II 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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