Preview Warm Up California Standards 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

California Standards NS2.3 Understand negative whole-number exponents. Multiply and divide expressions involving exponents with a common base. NS2.1 Multiply, divide, and simplify rational numbers by using exponent rules.

The following suggests a rule for multiplying powers with the same base. 24 • 22 = (2 • 2 • 2 • 2) • (2 • 2) = 26 a3 • a2 = (a • a • a) • (a • a) = a5 Notice that the sum of the exponents in each expression equals the exponent in the answer: 4 + 2 = 6 and 3 + 2 = 5.

Additional Example 1: Multiplying Powers with the Same Base Simplify each expression. Write your answer in exponential form. A. 66 • 63 6 6 + 3 Add exponents. 6 9 B. n5 • n7 n 5 + 7 Add exponents. n 12

A. 42 • 44 4 Add exponents. 4 B. x2 • x3 x Add exponents. x Check It Out! Example 1 Simplify each expression. Write your answer in exponential form. A. 42 • 44 4 2 + 4 Add exponents. 4 6 B. x2 • x3 x 2 + 3 Add exponents. x 5

The following suggests a rule for dividing powers with the same base. 3 6 32 = = 3 • 3 • 3 • 3 = 34 3  3 3  3  3  3  3  3 1 x 5 x3 = = x • x = x2 x  x  x x  x  x  x  x 1 Notice that the difference between the exponents in each expression equals the exponent in the answer: 6 – 2 = 4 and 5 – 3 = 2.

Additional Example 2: Dividing Powers with the Same Base Simplify each expression. Write your answer in exponential form. 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 Simplify each expression. Write your answer in exponential form. 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 To see what happens when you raise a power to a power, use the order of operations. RAISING A POWER TO A POWER Show the power inside the parentheses. (c3)2 = (c ● c ● c)2 Show the power outside the parentheses. = (c ● c ● c) ● (c ● c ● c) = c6 Simplify.

RAISING A POWER TO A POWER Reading Math (94)5 is read as “nine to the fourth power, to the fifth power.”

Additional Example 3: Raising a Power to a Power Simplify each expression. Write your answer in exponential form. 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 each expression. Write your answer in exponential form. C. D. (172)–20 2 3 12 • –3 Multiply exponents. 172 • –20 17–40 2 3 –36

A. (33)4 (33)4 33 • 4 Multiply exponents. 312 B. (48)2 (48)2 48 • 2 Check It Out! Example 3 Simplify each expression. Write your answer in exponential form. 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. Check It Out! Example 3 Simplify each expression. Write your answer in exponential form. C. D. (134)–10 1 4 11• –2 Multiply exponents. 134 • –10 13–40 1 4 –22

Lesson Quiz Simplify each expression. Write your answer in exponential form. 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 1 972 7. (9-8)9 8. (104)0 1