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

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

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

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

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

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The term 2 7 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. Course 3 2-6 Exponents 7 Exponent Base 2

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Course 3 2-6 Exponents Identify how many times 4 is a factor. 4 4 4 4 = 4 4 Write in exponential form. Additional Example 1A & 1B: Writing Exponents A. 4 4 4 4 Identify how many times d is a factor. d d d d d = d 5 B. d d d d d Read 4 4 as “4 to the 4 th power.” Reading Math

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

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Course 3 2-6 Exponents Identify how many times x is a factor. x x x x x = x 5 Write in exponential form. Try This: Example 1A & 1B 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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Course 3 2-6 Exponents Identify how many times –3 is a factor. (–3) (–3) (–3) (–3) = (–3) 4 Identify how many times 7 is a factor. 7 7 = 7 2 Try This: Example 1C & 1D C. (–3) (–3) (–3) (–3) D. 7 7 Write in exponential form.

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Course 3 2-6 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 Evaluate. Additional Example 2A & 2B: Evaluating Powers

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Course 3 2-6 Exponents D. 2 8 = 256 2 8 = 2 2 2 2 2 2 2 2 = 256 = (–4) (–4) (–4) (–4)(–4) 4 C. (–4) 4 Evaluate. Additional Example 2C & 2D: Evaluating Powers Continued Find the product of four –4’s. Find the product of eight 2’s.

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Course 3 2-6 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 Evaluate. Try This: Example 2A & 2B

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Course 3 2-6 Exponents D. 9 7 = 25 9 7 = 9 9 9 9 9 9 9 = 4,782,969 = (–5) (–5)(–5) 2 C. (–5) 2 Evaluate. Try This: Example 2C & 2D Find the product of two –5’s. Find the product of seven 9’s.

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Additional Example 3: Simplifying Expressions Containing Powers Course 3 2-6 Exponents = 47 Simplify (2 5 – 3 2 ) + 6(4). = (32 – 9) + 6(4) = (23) + 6(4) = 23 + 24 Evaluate the exponents. Subtract inside the parentheses. Multiply from left to right. Add from left to right.

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Course 3 2-6 Exponents Try This: Example 3 = –49 Simplify (3 2 – 8 2 ) + 2 3. = (9 – 64) + 2 3 = (–55) + 2 3 = –55 + 6 Evaluate the exponents. Subtract inside the parentheses. Multiply from left to right. Add from left to right.

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(7 2 – 3 7) 1212 Additional Example 4: Geometry Application Course 3 2-6 Exponents 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 formula (n 2 – 3n) to find the number of diagonals in a 7-sided figure. 1212

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

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(4 2 – 3 4) 1212 Try This: Example 4 Course 3 2-6 Exponents 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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Course 3 2-6 Exponents Verify your answer by sketching the diagonals. 2 diagonals Try This: Example 4 Continued

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

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Course 3 2-6 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 2 480

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