4-4 Laws of Exponents Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

4-4 Laws of Exponents Warm Up Evaluate b 2 for b = 4 4. n 2 r for n = 3 and r =

4-4 Laws of Exponents Problem of the Day Calculate 6 to the fourth power minus

4-4 Laws of Exponents Prep for MA.8.A.6.3 Simplify real number expressions using the laws of exponents. Also MA.8.A.6.4 Sunshine State Standards

4-4 Laws of Exponents The factors of a power, such as 7 4, can be grouped in different ways. Notice the relationship of the exponents in each product = 7 4 (7 7 7) 7 = = 7 4 (7 7) (7 7) = = 7 4

4-4 Laws of Exponents

4-4 Laws of Exponents Additional Example 1: Multiplying Powers with the Same Base A B. n 5 n 7 n 12 n Add exponents. Multiply. Write the product as one power.

4-4 Laws of Exponents D C Think: 2 = 2 1 Additional Example 1: Multiplying Powers with the Same Base Continued Multiply. Write the product as one power. Add exponents.

4-4 Laws of Exponents Check It Out: Example 1 A B. x 4 x 2 Multiply. Write the product as one power. = = = x 6 x x 4 x 2 =

4-4 Laws of Exponents D. p 2 p 2 C Check It Out: Example 1 Continued Multiply. Write the product as one power = = 15 3 p p 2 p 2 = = p 4

4-4 Laws of Exponents Notice what occurs when you divide powers with the same base = 5  5  55  5  5 5  5  5  5  5 = 5  5 = 5 2 = 5  5  55  5  5 5  5  5  5  5

4-4 Laws of Exponents Subtract exponents – Additional Example 2: Dividing Powers with the Same Base Divide. Write the quotient as one power. A. x 10 x 9 B. Subtract exponents. x 10 – 9 x Think: x = x 1

4-4 Laws of Exponents Check It Out: Example 2 Divide. Write the quotient as one power. A. B. n 8 n 5 9 = 9 7 =9 9 – = n 8 – 5 = n 3 n 8 n 5

4-4 Laws of Exponents RAISING A POWER TO A POWER Reading Math (9 ) is read as “nine to the fourth, to the fifth.” 5 4

4-4 Laws of Exponents Simplify. Multiply exponents. Additional Example 3: Raising a Power to a Power A. (5 4 ) 2 (5 4 ) B. (6 7 ) 9 (6 7 ) Multiply exponents.

4-4 Laws of Exponents Simplify. Multiply exponents. Additional Example 3: Raising a Power to a Power C. D. (17 2 ) –20 (17 2 ) – –20 17 –40 Multiply exponents – –3

4-4 Laws of Exponents Simplify. Check It Out: Example 3 A. (7 2 ) – 1 B. (7 – 1 ) 2 (7 2 ) – – 1 7 – = = (7 – 1 ) 2 7 –1 2 7 – = =

4-4 Laws of Exponents Simplify. Check It Out: Example 3 Continued C. D. (5 –2 ) – – = 1515 –8 = =58 = 390,625 (5 –2 ) –3 = 5 –2 –3 = 5 6 = 15,625

4-4 Laws of Exponents Additional Example 4: Application The speed of sound at sea level is x 10 2 meters per second. A ship that is 5 kilometers offshore sounds its horn. About how many seconds will pass before a person standing on shore will hear the sound? Write your answer in scientific notation.

4-4 Laws of Exponents Write 5 km as meters. Additional Example 4 Continued distance = rate x time It would take about 1.5 x 10 1 seconds for the sound to reach the shore. 5 km = ( x 10 2 ) x t 5000 = ( x 10 2 ) x t 5 x 10 3 = ( x 10 2 ) x t Write 5000 in scientific notation x x = t x 10 1  t

4-4 Laws of Exponents The diameter of a red blood cell is about 7.6 × millimeters. Thai has a slide with a 2-cm drop of red blood cells on it. Approximately how many cells are on the slide? Write your answer in scientific notation. (Hint: Find the ratio of the size of the drop, in millimeters, to the size of one cell.) Check It Out: Example 4

4-4 Laws of Exponents Check It Out: Example 4 Continued size of drop 7.6 x 10 –4 mm ≈ x 10 5 = x 10 4 size of red blood cell = number of red blood cells in drop; 2 cm = 7.6 x 10 –4 mm 2 mm = 7.6 x 10 –4 2 x 10 1 = x –4 cells

4-4 Laws of Exponents Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

4-4 Laws of Exponents Lesson Quiz Write the product or quotient as one power n 7 1. n 3  n t t 9 t 7 6. (m 2 ) 19 m (9 -8 ) 9 9 –72 8. (10 4 ) 0 1

4-4 Laws of Exponents 1. Write the product as one power. d 4  d 3 A. d 7 B. d 12 C. 7d D. 12d Lesson Quiz for Student Response Systems

4-4 Laws of Exponents 2. Write the product as one power. 4 4  4 3  4 2 A. 4 9 B C D Lesson Quiz for Student Response Systems

4-4 Laws of Exponents 3. Write the product as one power. (10 –1 ) 0 A. 10 –10 B. 0 C. 1 D. 10 Lesson Quiz for Student Response Systems