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

Warm Up Evaluate. 1. 33 27 2. 4 • 4 • 4 • 4 256 3. b2 for b = 4 16 4. n2r for n = 3 and r = 2 18

Problem of the Day Calculate 6 to the fourth power minus 56. 1240

Learn to apply the properties of exponents.

The factors of a power, such as 74, can be grouped in different ways 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 • 7 = 74 (7 • 7 • 7) • 7 = 73 • 71 = 74 (7 • 7) • (7 • 7) = 72 • 72 = 74

Additional Example 1: Multiplying Powers with the Same Base Multiply. Write the product as one power. A. 66 • 63 6 6 + 3 Add exponents. 6 9 B. n5 • n7 n 5 + 7 Add exponents. n 12

Additional Example 1: Multiplying Powers with the Same Base Continued Multiply. Write the product as one power. C. 25 • 2 2 5 + 1 Think: 2 = 2 1 2 6 Add exponents. D. 244 • 244 24 4 + 4 Add exponents. 24 8

A. 42 • 44 4 Add exponents. 4 B. x2 • x3 x Add exponents. x Check It Out: Example 1 Multiply. Write the product as one power. A. 42 • 44 4 2 + 4 Add exponents. 4 6 B. x2 • x3 x 2 + 3 Add exponents. x 5

Cannot combine; the bases are not the same. Check It Out: Example 1 Multiply. Write the product as one power. C. x5 • y2 Cannot combine; the bases are not the same. x5 • y2 D. 412 • 417 41 2 + 7 Add exponents. 41 9

Notice what occurs when you divide powers with the same base. 5 53 = 5  5  5 5  5  5  5  5 = 5 • 5 = 52

Additional Example 2: Dividing Powers with the Same Base Divide. Write the quotient as one power. 7 5 3 A. 7 5 – 3 Subtract exponents. 7 2 x 10 9 B. x 10 – 9 Subtract exponents. x Think: x = x 1

A. B. 9 9 9 Subtract exponents. 97 e e e Subtract exponents. e Check It Out: Example 2 Divide. Write the product as one power. 9 9 A. 9 2 9 9 – 2 Subtract exponents. 97 e 10 B. e 5 e 10 – 5 Subtract exponents. e 5

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

Additional Example 3: Raising a Power to a Power Simplify. A. (54)2 (54)2 = 54 • 2 Multiply exponents. = 58 B. (67)9 (67)9 = 67 • 9 Multiply exponents. = 663

Additional Example 3: Raising a Power to a Power Simplify. 2 3 12 –3 C. D. (172) –20 (172) –20 Multiply exponents. Multiply exponents. 2 3 12 • –3 = = 172 • –20 2 3 –36 = = 17–40

Additional Example: variables in the exponent  

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

= = C. D. (134) –10 Multiply exponents. Multiply exponents. Check It Out: Example 3 Simplify. 1 4 11 –2 C. D. (134) –10 (134) –10 Multiply exponents. Multiply exponents. 1 4 11• –2 = = 134 • –10 1 4 –22 = = 13–40

Lesson Quiz Write the product or quotient as one power. 1. n3  n4 n 7 2. 8 • 88 8 9 t9 t7 109 105 3. 4. 10 4 t 2 5. 32 • 33 • 35 3 10 6. (m2)19 m38 7. (9-8)9 8. (104)0 1 9–72