2 7 Properties of Exponents Warm Up Problem

2 -7 Properties of Exponents Warm Up Problem of the Day Lesson Presentation Course 3

2 -7 Properties of Exponents Warm Up Evaluate. 1. 33 27 2. 4 • 4 • 4 256 3. b 2 for b = 4 16 4. n 2 r for n = 3 and r = 2 18 Course 3

2 -7 Properties of Exponents Problem of the Day Calculate 6 to the fourth power minus 56. 1240 Course 3

2 -7 Properties of Exponents Learn to apply the properties of exponents and to evaluate the zero exponent. Course 3

2 -7 Properties of Exponents The factors of a power, such as 74, can be grouped in different ways. Notice the relationship of the exponents in each product. 7 • 7 • 7 = 74 (7 • 7) • 7 = 73 • 71 = 74 (7 • 7) • (7 • 7) = 72 • 72 = 74 Course 3

2 -7 Properties of Exponents MULTIPLYING POWERS WITH THE SAME BASE Words Numbers To multiply powers with 35 • 3 8 = the same base, 5 + 8 3 = 313 keep the base and add the exponents. Course 3 Algebra bm • bn = bm + n

2 -7 Properties of Exponents Additional Example 1 A & 1 B: Multiplying Powers with the Same Base Multiply. Write the product as one power. A. 66 • 63 66 + 3 69 Add exponents. B. n 5 • n 7 n 5 + 7 n 12 Add exponents. Course 3

2 -7 Properties of Exponents Additional Example 1: Multiplying Powers with the Same Base Continued Multiply. Write the product as one power. C. 25 • 2 25 + 1 26 Think: 2 = 2 1 Add exponents. D. 244 • 244 24 4 + 4 24 8 Course 3 Add exponents.

2 -7 Properties of Exponents Try This: Example 1 A & 1 B Multiply. Write the product as one power. A. 42 • 44 42 + 4 46 Add exponents. B. x 2 • x 3 x 2 + 3 x 5 Add exponents. Course 3

2 -7 Properties of Exponents Try This: Example 1 C & 1 D Multiply. Write the product as one power. C. x 5 • y 2 Cannot combine; the bases are not the same. D. 412 • 417 41 2 + 7 41 9 Course 3 Add exponents.

2 -7 Properties of Exponents Notice what occurs when you divide powers with the same base. 5 5 55 2 = 5 • 5 = = = 5 5 5 53 DIVIDING POWERS WITH THE SAME BASE Words To divide powers with the same base, keep the base and subtract the exponents. Course 3 Numbers 6 9 = 69 – 4 = 6 5 64 Algebra b m = bm – n bn

2 -7 Properties of Exponents Additional Example 2: Dividing Powers with the Same Base Divide. Write the product as one power. A. 5 7 3 7 75 – 3 7 Subtract exponents. 2 10 B. x 9 x x 10 – 9 x Course 3 Subtract exponents. Think: x 1 = x

2 -7 Properties of Exponents Try This: Example 2 Divide. Write the product as one power. A. 99 92 99 – 2 97 B. e 10 e 5 e 10 – 5 5 e Course 3 Subtract exponents.

2 -7 Properties of Exponents When the numerator and denominator have the same base and exponent, subtracting the exponents results in a 0 exponent. 2 4 2 – 2 = 40 = 1= 4 42 This result can be confirmed by writing out the factors. 42 42 Course 3 (4 • 4) = 1 =1 = = (4 • 4) 1 (4 • 4)

2 -7 Properties of Exponents Helpful Hint 00 does not exist because 00 represents a quotient of the form 0 n. 0 n But the denominator of this quotient is 0, which is impossible, since you cannot divide by 0. Course 3

2 -7 Properties of Exponents THE ZERO POWER Words Numbers The zero power of any number except 0 equals 1. 1000 = 1 Course 3 (– 7)0 = 1 Algebra a 0= 1, if a 0

2 -7 Properties of Exponents Additional Example 3: Astronomy Application A light-year, or the distance light travels in one year, is almost 1018 centimeters. To convert this number to kilometers, you must divide by 105. How many kilometers is a light-year? 10 18 10 5 10 18 - 5 Subtract exponents. 13 10 A light-year is almost 1013 km. Course 3

2 -7 Properties of Exponents Try This: Example 3 A ship has 107 kilograms of grain loaded into its cargo hold. A metric ton is 103 kilograms. How many metric tons of grain were loaded? 10 103 7 The weight in metric tons is equal to the weight in kilograms divided by 10 3 kilograms per metric ton. 107 - 3 Subtract exponents. 10 4 The ship had 104 metric tons of grain loaded. Course 3

2 -7 Properties of Exponents Lesson Quiz: Part 1 Write the product or quotient as one power 1. n 3 n 4 n 7 2. 8 • 88 89 109 3. 105 104 t 9 4. t 7 t 2 5. 33 • 32 • 35 Course 3 310

2 -7 Properties of Exponents Lesson Quiz: Part 2 6. A school would like to purchase new globes. They can get six dozen for $705. 80 from Company A. From Company B, they can buy a half gross for $725. 10. Which company should they buy from? (1 gross = 122 items) Company A Course 3