ofof Exponents 4 3 Properties Exponents Warm Up

ofof Exponents 4 -3 Properties Exponents Warm Up Problem of the Day Lesson Presentation Course 33

4 -3 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

4 -3 Properties of Exponents Problem of the Day Calculate 6 to the fourth power minus 56. 1240 Course 3

4 -3 Properties of Exponents Learn to apply the properties of exponents. Course 3

4 -3 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

4 -3 Properties of Exponents Course 3

4 -3 Properties of Exponents Example 1: 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

4 -3 Properties of Exponents 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.

4 -3 Properties of Exponents Check It Out: Example 1 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

4 -3 Properties of Exponents Check It Out: Example 1 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.

4 -3 Properties of Exponents Notice what occurs when you divide powers with the same base. 5 5 55 2 = 5 • 5 = = = 5 5 5 53 Course 3

4 -3 Properties of Exponents Example 2: Dividing Powers with the Same Base Divide. Write the quotient 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

4 -3 Properties of Exponents Check It Out: 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.

4 -3 Properties of Exponents RAISING A POWER TO A POWER Reading Math 4 5 (9 ) is read as “nine to the fourth, to the fifth. ” Course 3

4 -3 Properties of Exponents Example 3: Raising a Power to a Power Simplify. A. (54)2 = 54 • 2 Multiply exponents. = 58 B. (67)9 = 67 • 9 Multiply exponents. = 663 Course 3

4 -3 Properties of Exponents Example 3: Raising a Power to a Power Simplify. C. (172) – 20 = 172 • – 20 = 17– 40 Course 3 Multiply exponents.

4 -3 Properties of Exponents Check It Out: Example 3 Simplify. A. (33)4 = 33 • 4 Multiply exponents. = 312 B. (48)2 = 48 • 2 Multiply exponents. = 416 Course 3

4 -3 Properties of Exponents Check It Out: Example 3 Simplify. D. (134) – 10 = 134 • – 10 = 13– 40 Course 3 Multiply exponents.

4 -3 Properties of Exponents Lesson Quiz Write the product or quotient as one power. 1. n 3 n 4 3. Course 3 109 105 n 7 104 2. 8 • 88 89 t 9 4. t 7 t 2 5. 32 • 33 • 35 310 6. (m 2)19 m 38 7. (9 -8)9 9– 72 8. (104)0 1