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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 !. ?. ?. ?.
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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 ? ?
= 1 1 = 10 10 • 10 1 = = = 0.1 1 10 = 0.01 100 Let’s practice Simplify the powers of 10. A. 10–2 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?
1 1 1 = = = –1000 16 125 Let’s practice A. 5–3 = B. (–10)–3 = C. 4–2 =
Rules: Zero Exponent: Negative Exponent: (except for which is 0)
Zero Exponents =1 • 100 • 150 • x0 • (-5)0 • x0y0 =1 =1 =1 =11=1
Negative Coefficients 1. 2. 3. 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
1 8 1 23 7 8 5 5 – + 1 5 – + 1 What about this? Simplify 5 – (6 – 4)–3+ (–2)0. 5 – (6 – 4)–3+ (–2)0 5 – (2)–3+ (–2)0
a) b) Remember the Rules?? Rewriting Fractions using negative exponents(going backwards) Negative Exponent:
Lesson Quiz Simplify the powers of 10. 0.001 1. 10–3 0.0000001 2. 10–7 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.