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2-6 Exponents Warm Up Problem of the Day Lesson Presentation Course 3 2-6 Exponents Warm Up Find the product. 1. 5 • 5 • 5 • 5 625 2. 3 • 3 • 3 27 3. (–7) • (–7) • (–7) –343 4. 9 • 9 81 Course 3 2-6 Exponents Problem of the Day What two positive integers when multiplied together also equal the sum of the same two numbers? 2 and 2 Course 3 2-6 Exponents Learn to evaluate expressions with exponents. Course 3 2-6 Exponents Vocabulary power exponential form exponent base Course 3 2-6 Exponents 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 2 Course 3 7 2-6 Exponents Additional Example 1A & 1B: Writing Exponents Write in exponential form. A. 4 • 4 • 4 • 4 4 • 4 • 4 • 4 = 44 Identify how many times 4 is a factor. B. d • d • d • d • d d • d • d • d • d = d5 Identify how many times d is a factor. Reading Math Read 44 as “4 to the 4th power.” Course 3 2-6 Exponents Additional Example 1C & 1D: Writing Exponents Write in exponential form. C. (–6) • (–6) • (–6) (–6) • (–6) • (–6) = (–6)3 Identify how many times –6 is a factor. D. 5 • 5 5 • 5 = 52 Identify how many times 5 is a factor. Course 3 2-6 Exponents Try This: Example 1A & 1B Write in exponential form. A. x • x • x • x • x x • x • x • x • x = x5 Identify how many times x is a factor. B. d • d • d d • d • d = d3 Course 3 Identify how many times d is a factor. 2-6 Exponents Try This: Example 1C & 1D Write in exponential form. C. (–3) • (–3) • (–3) • (–3) (–3) • (–3) • (–3) • (–3) = (–3)4 D. 7 • 7 7 • 7 = 72 Course 3 Identify how many times –3 is a factor. Identify how many times 7 is a factor. 2-6 Exponents Additional Example 2A & 2B: Evaluating Powers Evaluate. Find the product of five 3’s. A. 35 35 = 3 • 3 • 3 • 3 • 3 = 243 B. (–3)5 Find the product of five –3’s. (–3)5 = (–3) • (–3) • (–3) • (–3) • (–3) = –243 Helpful Hint Always use parentheses to raise a negative number to a power. Course 3 2-6 Exponents Additional Example 2C & 2D: Evaluating Powers Continued Evaluate. C. (–4)4 Find the product of four –4’s. (–4)4 = (–4) • (–4) • (–4) • (–4) = 256 D. 28 Find the product of eight 2’s. 28 = 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 = 256 Course 3 2-6 Exponents Try This: Example 2A & 2B Evaluate. Find the product of four 7’s. A. 74 74 = 7 • 7 • 7 • 7 = 2401 B. (–9)3 Find the product of three –9’s. (–9)3 = (–9) • (–9) • (–9) = –729 Course 3 2-6 Exponents Try This: Example 2C & 2D Evaluate. Find the product of two –5’s. C. (–5)2 (–5)2 = (–5) • (–5) = 25 Find the product of seven 9’s. D. 97 97 = 9 • 9 • 9 • 9 • 9 • 9 • 9 = 4,782,969 Course 3 2-6 Exponents 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. = 23 + 24 Multiply from left to right. = 47 Add from left to right. Course 3 2-6 Exponents Try This: Example 3 Simplify (32 – 82) + 2 • 3. = (9 – 64) + 2 • 3 Evaluate the exponents. = (–55) + 2 • 3 Subtract inside the parentheses. = –55 + 6 Multiply from left to right. = –49 Add from left to right. Course 3 2-6 Exponents Additional Example 4: Geometry Application 1 Use the formula 2 (n2 – 3n) to find the number of diagonals in a 7-sided figure. 1 2 1 2 1 2 1 2 1 2 (n2 – 3n) (72 – 3 • 7) Substitute the number of sides for n. (49 – 3 • 7) Evaluate the exponent. (49 – 21) Multiply inside the parentheses. (28) Subtract inside the parentheses. 14 diagonals Course 3 Multiply 2-6 Exponents Additional Example 4 Continued Verify your answer by sketching the diagonals. 14 Diagonals Course 3 2-6 Exponents Try This: Example 4 Use the formula 1 (n2 – 3n) to find the number of 2 diagonals in a 4-sided figure. 1 2 1 2 1 2 1 2 1 2 (n2 – 3n) (42 – 3 • 4) Substitute the number of sides for n. (16 – 3 • 4) Evaluate the exponents. (16 – 12) Multiply inside the parentheses. (4) Subtract inside the parentheses. 2 diagonals Course 3 Multiply 2-6 Exponents Try This: Example 4 Continued Verify your answer by sketching the diagonals. 2 diagonals Course 3 2-6 Exponents Lesson Quiz: Part 1 Write in exponential form. 1. n • n • n • n 2. (–8) • (–8) • (–8) 3. Evaluate (–4)4 4. Simplify 99 – 3(4 • 23). Course 3 n4 (–8)3 256 3 2-6 Exponents 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 Course 3