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4-1 Exponents Warm Up Problem of the Day Lesson Presentation Lesson Quizzes 4-1 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 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 4-1 Exponents Learn to evaluate expressions with exponents. 4-1 Exponents Vocabulary exponential form exponent base power 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 33 represent the same power. Exponent Base 2 7 4-1 Exponents Additional Example 1: 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. (–6) • (–6) • (–6) (–6) • (–6) • (–6) = (–6)3 Identify how many times –6 is a factor. Reading Math Read –(63) as “ negative 6 to the 3rd power” or “negative 6 cubed”. 4-1 Exponents Additional Example 1: Writing Exponents Write in exponential form. C. 5 • 5 • d • d • d • d 5 • 5 • d • d • d • d = 52d4 Identify how many times 5 and d are used as a factor. 4-1 Exponents Check It Out: Example 1 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 Identify how many times d is a factor. 4-1 Exponents Check It Out: Example 1 Write in exponential form. C. 7 • 7 • b • b 2 7•7•b•b=7b 2 Identify how many times 7 and b are used as a factor. 4-1 Exponents Additional Example 2: Simplifying Powers Simplify. Find the product of five 3’s. A. 35 35 = 3 • 3 • 3 = 243 • 5 B. (–3) Find the product of five –3’s. 3•3 (–3)5 = (–3) • (–3) • (–3) • (–3) • (–3) = –243 Helpful Hint Always use parentheses to raise a negative number to a power. 4-1 Exponents Additional Example 2: Simplifying Powers Simplify. C. (–4)4 (–4)4= (–4) • (–4) • (–4) • (–4) = 256 D. Find the product of four –4’s. Find the product of eight 1/2’s. 4-1 Exponents Check It Out: Example 2 Simplify. 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 4-1 Exponents Check It Out: Example 2 Simplify. C. –(5)2 –(5)2 = –(5) • (5) = –25 Find the product of two 5’s and then make the answer negative. D. 97 Find the product of 97 = 9 • 9 • 9 • 9 • 9 • 9 • 9 = 4,782,969 seven 9’s. 4-1 Exponents Additional Example 3: Using the Order of Operations Evaluate x(yx – zy) + xy for x = 4, y = 2, and z = 3. x(yx – zy) + xy 4(24 – 32) + 42 Substitute 4 for x, 2 for y, and 3 for z. 4(16 – 9) + 16 Evaluate the exponent. 4(7) + 16 Subtract inside the parentheses. 28 + 16 Multiply from left to right. 44 Add. 4-1 Exponents Check It Out: Example 3 Evaluate z – 7(2x – xy) for x = 5, y = 2, and z = 60. z – 7(2x – xy) 60 – 7(25 – 52) Substitute 5 for x, 2 for y, and 60 for z. 60 – 7(32 – 25) Evaluate the exponent. 60 – 7(7) Subtract inside the parentheses. 60 – 49 Multiply from left to right. 11 Subtract. 4-1 Exponents Additional Example 4: Geometry Application 1 Use the expression 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 Multiply 4-1 Exponents Additional Example 4 Continued A 7-sided figure has 14 diagonals. You can verify your answer by sketching the diagonals. 4-1 Exponents Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems 4-1 Exponents Warm-up: Page 159 # 1-10 all Homework: Page 164 # 1-30 all *no calculator on warm-up or homework* 4-1 Exponents Lesson Quiz: Part I Write in exponential form. 1. n• n • 2. (–8) • n4 n• n (–8) • (–8) 3. Evaluate (–4)4 4. Evaluate x –213 • • (h) (–8)3h 256 z – yx for x = 5, y = 3, and z = 6. 4-1 Exponents Example 5 1 Use the formula 2 (n2 – 3n) to find the number of 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 Multiply. 4-1 Exponents A 4-sided figure has 2 diagonals. You can verify your answer by sketching the diagonals. 4-1 Exponents 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 4-1 Exponents Lesson Quiz for Student Response Systems 1. Write g• g A. 5g B. g + 5 C. g5 D. g5 • g• g• g in exponential form. 4-1 Exponents Lesson Quiz for Student Response Systems 2. Evaluate (–3)4. A. 12 B. –12 C. 81 D. –81 4-1 Exponents Lesson Quiz for Student Response Systems 3. Evaluate gh + 3k – gk for g = 2, h = 4, and k = 3. A. 6 B. 7 C. 9 D. 11