Warmup Simplify the expression Lesson 4 2 Integer

Warm-up Simplify the expression

Lesson 4. 2 Integer exponents

Objectives Ø Understand negative whole number exponents and zero exponents. (NS 2. 1) Ø Interpret negative powers as repeated division or multiplication by the multiplicative inverse. (AF 2. 1)

Patterns are COOL! COOL ? ? 2 ? ? 2

Each time we cut it in half!!

Let’s practice Simplify the powers of 10. A. 10 = 1 10 • 10 = B. 10– 1 = 1 10 – 2 1 = 0. 01 100 = 1 = 0. 1 10

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 Using rules of exponents 11

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

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

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

Zero Exponents • • • 100 =1 150 =1 x 0 =1 (-5)0 =1 x 0 y 0 =1 1=1

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

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

What about this? Simplify 5 – (6 – 4)– 3 + (– 2)0 5 – (2)– 3 + (– 2)0 5 – 13 + 1 2 1 8 5– +1 5 7 8

Remember the Rules? ? Rewriting Negative Exponent: Fractions using negative a) exponents (going backwards) 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 Simplify. 3. (– 6)– 2 4. 4 • 5. 80 2– 3 1 36 + 10– 1 – (11 – 24)– 2 3 5 24 25 6. Evaluate (4 w)– 2 + w– 1 for w = 4. 65 256