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4-1 Exponents Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

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

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4-1 Exponents Problem of the Day What two positive integers when multiplied together also equal the sum of the same two numbers? 2 and 2

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4-1 Exponents Learn to evaluate expressions with exponents.

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4-1 Exponents Vocabulary exponential form exponent base power

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4-1 Exponents 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 3 3 represent the same power. 7 Exponent Base 2

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

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4-1 Exponents Identify how many times 5 and d are used as a factor. Additional Example 1: Writing Exponents C. 5 5 d d d d Write in exponential form. 5 5 d d d d = 5 2 d 4

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4-1 Exponents Identify how many times x is a factor. x x x x x = x 5 Write in exponential form. Check It Out: Example 1 A. x x x x x Identify how many times d is a factor. d d d = d 3 B. d d d

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4-1 Exponents Identify how many times 7 and b are used as a factor. 7 7 b b = 7 2 b 2 Check It Out: Example 1 C. 7 7 b b Write in exponential form.

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4-1 Exponents A. 3 5 = 243 3 5 = 3 3 3 3 3 Find the product of five 3’s. = –243 = (–3) (–3) (–3) (–3) (–3) (–3) 5 Find the product of five –3’s. B. (–3) 5 Always use parentheses to raise a negative number to a power. Helpful Hint Simplify. Additional Example 2: Simplifying Powers

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4-1 Exponents D. = 256 = (–4) (–4) (–4) (–4) (–4) 4 C. (–4) 4 Simplify. Additional Example 2: Simplifying Powers Find the product of four –4’s. Find the product of eight 1/2’s.

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4-1 Exponents A. 7 4 = 2401 7 4 = 7 7 7 7 Find the product of four 7’s. = –729 = (–9) (–9) (–9) (–9) 3 Find the product of three –9’s. B. (–9) 3 Simplify. Check It Out: Example 2

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4-1 Exponents D. 9 7 = – 25 9 7 = 9 9 9 9 9 9 9 = 4,782,969 = –(5) (5) –(5) 2 C. –(5) 2 Simplify. Check It Out: Example 2 Find the product of two 5’s and then make the answer negative. Find the product of seven 9’s.

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4-1 Exponents Additional Example 3: Using the Order of Operations 4(7) + 16 Substitute 4 for x, 2 for y, and 3 for z. Evaluate the exponent. Subtract inside the parentheses. Multiply from left to right. 4(2 4 – 3 2 ) + 4 2 4(16 – 9) + 16 28 + 16 Evaluate x(y x – z y ) + x for x = 4, y = 2, and z = 3. y x(y x – z y ) + x y Add. 44

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4-1 Exponents Check It Out: Example 3 60 – 7(7) Substitute 5 for x, 2 for y, and 60 for z. Evaluate the exponent. Subtract inside the parentheses. Multiply from left to right. 60 – 7(2 5 – 5 2 ) 60 – 7(32 – 25) 60 – 49 Evaluate z – 7(2 x – x y ) for x = 5, y = 2, and z = 60. z – 7(2 x – x y ) Subtract. 11

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4-1 Exponents (7 2 – 3 7) 1212 Additional Example 4: Geometry Application Evaluate the exponent. Multiply inside the parentheses. Multiply Substitute the number of sides for n. Subtract inside the parentheses. 14 diagonals (49 – 21) 1212 (n 2 – 3n) 1212 (49 – 3 7) 1212 (28) 1212 Use the expression (n 2 – 3n) to find the number of diagonals in a 7-sided figure. 1212

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4-1 Exponents A 7-sided figure has 14 diagonals. You can verify your answer by sketching the diagonals. Additional Example 4 Continued

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4-1 Exponents (4 2 – 3 4) 1212 Check It Out: Example 4 Evaluate the exponents. Multiply inside the parentheses. Multiply. Substitute the number of sides for n. Subtract inside the parentheses. 2 diagonals (16 – 12) 1212 (n 2 – 3n) 1212 (16 – 3 4) 1212 (4) 1212 Use the formula (n 2 – 3n) to find the number of diagonals in a 4-sided figure. 1212

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4-1 Exponents A 4-sided figure has 2 diagonals. You can verify your answer by sketching the diagonals. Check It Out: Example 4 Continued

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4-1 Exponents Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

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

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4-1 Exponents 5. A population of bacteria doubles in size every minute. The number of bacteria after 5 minutes is 15 2 5. How many are there after 5 minutes? Lesson Quiz: Part II 480

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4-1 Exponents 1. Write g g g g g in exponential form. A. 5g B. g + 5 C. g 5 D. g5 Lesson Quiz for Student Response Systems

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4-1 Exponents 2. Evaluate (–3) 4. A. 12 B. –12 C. 81 D. –81 Lesson Quiz for Student Response Systems

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4-1 Exponents 3. Evaluate gh + 3k – g k for g = 2, h = 4, and k = 3. A. 6 B. 7 C. 9 D. 11 Lesson Quiz for Student Response Systems

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