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LO: I will explore and simplify rational numbers using patterns of nonzero integer exponents. Adv. Exploring Rational Numbers-Nonzero Integer Exponents Evaluate each expression for the given values of the variables . 1. x 3 y 2 for x = –1 and y = 10

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  1. LO: I will explore and simplify rational numbers using patterns of nonzero integer exponents. Adv. Exploring Rational Numbers-Nonzero Integer Exponents Evaluate each expression for the given values of the variables. 1.x 3y 2for x = –1 and y = 10 2. for x = 4 and y = (–7) Write each number as a power of the given base. 3. 64; base 4 Launch

  2. You have seen positive exponents. Recall that to simplify 32, use 3 as a factor 2 times: 32 = 3  3 = 9. But what does it mean for an exponent to be negative or 0? You can use a table and look for a pattern to make a conjecture. DECLINE

  3. Reasoning Strategies-Using Patterns. The pattern in the t-graph will help you evaluate powers with nonzero integer exponents. Explore

  4. Note: the phrase “nonzero number” in the previous table. This is because 00 and 0 raised to a negative power are both undefined. For example, if you use the pattern given above in the table with a base of 0, you would get 00 = . Also, 0–6 would be = . Since division by 0 is undefined, neither value exists. RECALL: Any nonzero number raised to the zero power is 1. Skills & Vocabulary

  5. One cup is 2–4 gallons. Simplify this expression. A sand fly may have a wingspan up to 5–3 m. One cup is equal to gal. A sand fly may have a wingspan of m. A square foot is 3–2 square yards. Simplify this expression. One square foot is equal to______ square yards. Real-life Connections

  6. for a = 6 and b = 3 Evaluate the expression for the given value of the variable. x –2 for x = 4 p –3 for p = 4 –2a0 b -4 for a = 5 and b = –3 2–6 (–7) –3 60 –112 x –4 for x =10 Rigor

  7. A. 4–3 a. 10–4 Caution In (–3)–4, the base is negative because the negative sign is inside the parentheses. In –3–4 the base (3) is positive. B. 70 b. (–2)–4 C. (–5)–4 c. (–2)–5 D. –5–4 d. –2–5

  8. Real Life Application 27. 28. 4.2 & SR p175 #49-59even

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