Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

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

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

Learn to evaluate expressions with exponents.

Vocabulary exponential form exponent base power

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

Additional Example 1: Writing Exponents Write in exponential form. A. 4 • 4 • 4 • 4 Identify how many times 4 is a factor. 4 • 4 • 4 • 4 = 44 B. (–6) • (–6) • (–6)‏ Identify how many times –6 is a factor. (–6) • (–6) • (–6) = (–6)3 Read –(63) as “ negative 6 to the 3rd power” or “negative 6 cubed”. Reading Math

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 5 • 5 • d • d • d • d = 52d4

Write in exponential form. Check It Out: Example 1 Write in exponential form. A. x • x • x • x • x Identify how many times x is a factor. x • x • x • x • x = x5 B. d • d • d Identify how many times d is a factor. d • d • d = d3

Write in exponential form. 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 • b • b = 72b2

Additional Example 2: Simplifying Powers Find the product of five 3’s. 35 = 3 • 3 • 3 • 3 • 3 = 243 B. (–3)5 Find the product of five –3’s. = (–3) • (–3) • (–3) • (–3) • (–3)‏ (–3)5 = –243 Helpful Hint Always use parentheses to raise a negative number to a power.

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

Simplify. A. 74 Find the product of four 7’s. 74 = 7 • 7 • 7 • 7 Check It Out: Example 2 Simplify. A. 74 Find the product of four 7’s. 74 = 7 • 7 • 7 • 7 = 2401 B. (–9)3 Find the product of three –9’s. = (–9) • (–9) • (–9)‏ (–9)3 = –729

Simplify. C. –(5)2 = –(5) • (5)‏ –(5)2 = –25 D. 97 Check It Out: Example 2 Simplify. C. –(5)2 Find the product of two 5’s and then make the answer negative. = –(5) • (5)‏ –(5)2 = –25 D. 97 Find the product of seven 9’s. 97 = 9 • 9 • 9 • 9 • 9 • 9 • 9 = 4,782,969

Additional Example 3: Using the Order of Operations Evaluate x(yx – zy) + x for x = 4, y = 2, and z = 3. y x(yx – zy) + xy Substitute 4 for x, 2 for y, and 3 for z. 4(24 – 32) + 42 4(16 – 9) + 16 Evaluate the exponent. 4(7) + 16 Subtract inside the parentheses. 28 + 16 Multiply from left to right. 44 Add.

Evaluate z – 7(2x – xy) for x = 5, y = 2, and z = 60. Check It Out: Example 3 Evaluate z – 7(2x – xy) for x = 5, y = 2, and z = 60. z – 7(2x – xy) 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. 11 Subtract.

Additional Example 4: Geometry Application 1 2 Use the expression (n2 – 3n) to find the number of diagonals in a 7-sided figure. (n2 – 3n)‏ 1 2 (72 – 3 • 7)‏ 1 2 Substitute the number of sides for n. (49 – 3 • 7)‏ 1 2 Evaluate the exponent. (49 – 21)‏ 1 2 Multiply inside the parentheses. (28)‏ 1 2 Subtract inside the parentheses. 14 diagonals Multiply

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

(n2 – 3n)‏ (42 – 3 • 4)‏ (16 – 3 • 4)‏ (16 – 12)‏ (4)‏ 2 diagonals Check It Out: Example 4 1 2 Use the formula (n2 – 3n) to find the number of diagonals in a 4-sided figure. (n2 – 3n)‏ 1 2 (42 – 3 • 4)‏ 1 2 Substitute the number of sides for n. (16 – 3 • 4)‏ 1 2 Evaluate the exponents. (16 – 12)‏ 1 2 Multiply inside the parentheses. (4)‏ 1 2 Subtract inside the parentheses. 2 diagonals Multiply.

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

Lesson Quiz for Student Response Systems Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems 21

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

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

Lesson Quiz for Student Response Systems 1. Write g• g • g• g• g in exponential form. A. 5g B. g + 5 C. g5 D. g5 24

Lesson Quiz for Student Response Systems 2. Evaluate (–3)4. A. 12 B. –12 C. 81 D. –81 25

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 26