Warm-up Simplify the expression

Lesson 4.2 Integer exponents

Objectives Understand negative whole number exponents and zero exponents. (NS 2.1) Interpret negative powers as repeated division or multiplication by the multiplicative inverse. (AF 2.1)

Patterns are COOL! ? ? ? ? ? ? ? ? 2 2 ? ?

Each time we cut it in half!!

Let’s practice = A. 10–2 = = 0.01 = B. 10–1 = = 0.1 Simplify the powers of 10. = 1 100 = 0.01 = 1 10 • 10 A. 10–2 = 1 10 = = 0.1 1 10 B. 10–1

Negative Exponents You do not want to have negative exponents in your answers, so you get rid of them by flipping the exponent like reciprocals. If the negative exponent is on top, move to the bottom. If the negative exponent is on bottom, move to the top. 1

Division & Negative Exponents 1 1 Using rules of exponents

How do you change the negative exponent to a positive exponent?

Let’s practice 125 1 = A. 5–3 = –1000 1 = B. (–10)–3 = 16 1 = C. 4–2 =

Rules: (except for which is 0) Zero Exponent: Negative Exponent:

Zero Exponents 100 150 x0 (-5)0 x0y0 =1 =1 =1 =1 =11=1

1. 2. 3. Negative Coefficients RULE: Negative signs are attached to the COEFFICIENT, unless in parenthesis.

You try! 1.3-4 4. 2-1 2.-10-3 5. 3. x-5 6.-14 x-4

What about this? Simplify 5 – (6 – 4)–3 + (–2)0. 5 – (6 – 4)–3 + (–2)0 5 – (2)–3 + (–2)0 5 – + 1 1 23 5 – + 1 1 8 5 7 8

Rewriting Fractions using negative exponents (going backwards) Remember the Rules?? Negative Exponent: Rewriting Fractions using negative exponents (going backwards) a) b)

Summary: Explain what you learned about negative exponent?

Lesson Quiz Simplify the powers of 10. 1. 10–3 0.001 2. 10–7 0.0000001 1. 10–3 0.001 2. 10–7 0.0000001 Simplify. 1 36 3. (–6)–2 3 5 4. 4 • 2–3 + 10–1 24 25 5. 80 – (11 – 24)–2 65 256 6. Evaluate (4w)–2 + w–1 for w = 4.