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Exponents Course: Understanding and Evaluating Exponential Expressions

Learn to evaluate expressions with exponents, understand the exponential form, base, and power concept, and practice evaluating powers with examples. Enhance your math skills with interactive lessons and quizzes.

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Exponents Course: Understanding and Evaluating Exponential Expressions

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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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