Warm Up Find the product. 1. 5 • 5 • 5 • 5 625 2. 3 • 3 • 3 27 sefgdfg Warm Up Find the product. Remember to subtract a negative number you add the opposite. 5. -5 – (-15) 6. 6 – (-10) 1. 5 • 5 • 5 • 5 625 2. 3 • 3 • 3 27 10 16 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. sefgdfg Learn to evaluate expressions with exponents.

sefgdfg Vocabulary exponential form exponent base power

sefgdfg exponential form: When a number is represented with an exponent. 42, 25 power: The number produced by raising a base to an exponent. Both 27 and 33 represent the same power. Exponent Base 7 2

Expanded Form Base Number of factors Power Evaluate 3 • 3 3 2 32 9 2 • 2 • 2 • 2 4 24 6 • 6 • 6 6 4 • 4 • 4 • 4 7 • 7 • 7 • 7 x4 Ω 42 1 5 a

What is the value of any power that has 1 as its base? Explain. Write Pair Share…. Identify the base and the exponent in the power 54. Explain how to evaluate 54. What is the value of any power that has 1 as its base? Explain. Write the number 1000 using an exponent. Write the number 10,000 using an exponent. Complete the statements. For each expression, identify the base and the exponent. How do the parentheses make the first expression different from the second expression? (4x)2 = (4x) • ____ 4x2 = 4 • ____ • ____ base: ____ exponent: _____ exponent: ______

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

Write in exponential form. sefgdfg Write in exponential form. Identify how many times 5 and d are used as a factor. C. 5 • 5 • d • d • d • d 52d4

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

Write in exponential form. sefgdfg 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 sefgdfg Additional Example 2: Simplifying Powers Simplify. A. 35 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 sefgdfg Additional Example 2: Simplifying Powers Simplify. 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 sefgdfg 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 sefgdfg 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 sefgdfg 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. sefgdfg 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 sefgdfg 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 sefgdfg 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 sefgdfg 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 sefgdfg 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 sefgdfg Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems 21

Write in exponential form. sefgdfg 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

sefgdfg 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 sefgdfg 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 sefgdfg 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 sefgdfg 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