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8.3 Define and Use Zero and Negative Exponents Goal Use zero and negative exponents. QUESTION How can you simplify expressions with zero or negative exponents? EXPLORE Evaluate powers with zero and negative exponents STEP 1 Find a pattern Complete the tables for the powers of 2 and 3. Exponent, n Value of 2n Exponent, n 4 16 4 3 3 2 2 1 1 Value of 3n 81 As you read the tables from the bottom up, you see that each time the exponent is increased by 1, the value of the power is multiplied by the base. What can you say about the exponents and the values of the powers as you read the table from the top down? STEP 2 Extend the pattern Complete the tables using the pattern you observed in Step 1. Exponent, n Power, 2n Exponent, n Power, 3n 3 8 3 27 2 2 1 1 0 0 –1 –1 –2 –2 DRAW CONCLUSIONS Use your observations to complete these exercises 1. Find 2n and 3n for n = –3, –4, and –5. 2. What appears to be the value of a 0 for any nonzero number a? Page 1 3. Write each power in the tables above as a power with a positive exponent. For example, you 1 can write 3–1 as 31 . DEFINITION OF ZERO AND NEGATIVE EXPONENTS Words Algebra 0 a to the zero power a a is 1. a0 = ____, a ≠ 0 Example 50 = ____ a–n is the reciprocal of an. a–n = ____ ,a ≠ 0 2–1 = ____ an is the reciprocal of a–n. an = ____ ,a ≠ 0 25 = ____ Example 1 - Use definition of zero and negative exponents Evaluate the expression. a. 2–3 = b. (-10)° = 3 c. 1 4 d. 0–7 = SUMMARY OF PROPERTIES OF EXPONENTS Let a and b be real numbers, and let m and n be integers. am. an = a ______ ______________________________ property (am)n = a ____ ______________________________ property (ab)m = _______ ______________________________ property m a = a _____ , a ≠ 0 an m a = ____ b ≠ 0 b ______________________________ property ______________________________ property b Example 2 Evaluate exponential expressions a) (-5)4 • (-5)– 4 = Page 2 b) (5-2)–2 = c) 1 = 4 2 d) 32 = 31 Checkpoint Evaluate the expression. 1) 1 1 8 2) 1 3 2 1 3) b66 4) (5–1)2 Example 3 - Use properties of exponents Simplify the expression 2𝑤 −3 𝑥 (2𝑤𝑥)2 Write your answer using only positive exponents. = 3 (2𝑤𝑥)2 Page Solution 2𝑤 −3 𝑥 Checkpoint Simplify the expression. 𝟓) 𝟔𝒇𝒈−𝟒 𝟐𝒇𝟐 𝒈 Page 4 6) (𝟑𝒚𝒛𝟐 )−𝟐