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6-1 Integer Exponents Algebra 1 Warm Up: Evaluate each expression for the given values of the variables. 1. 𝑥 3 𝑦 2 for 𝑥 = −1 and 𝑦 = 10 2. 3𝑥 2 𝑦2 for 𝑥 = 4 and y= (−7) Write each number as a power of the given base. 3. 64; base 4 4. 27; base 3 Objectives: Evaluate expression containing zero and integer exponents. Simplify expressions containing zero and integer exponents. What does it mean for an exponent to be a negative or 0? You can use a table and look for a pattern to find out. WORDS NUMBERS Zero exponent – Any nonzero number 30 = raised to the ______ exponent is _____. 1230 = ALGEBRA If 𝑥 ≠ 0, then 𝑥 0 = (−16)0 = 3 0 ( ) = 7 Negative exponent - nonzero number raised to a negative exponent is equal to _______ divided by that _____________ raised to the opposite (_____________) 3−2 = If 𝑥 ≠ 0 and n is an integer, then 𝑥 −𝑛 = 2−4 = exponent. Examples: Application 1. One cup is 2−4 gallons. Simplify this expression. Check It Out! 1. A sand fly may have a wingspan up to 5−3 m. Simplify this expression. Example 2: Zero and Negative Exponents Simplify. A) 43 B) 70 C) (5)4 D) 54 d) 25 **Remember: In order to have a negative base, it must be in ______________________________. Check It Out! Example 2: Simplify. a) 10 4 b) (2)4 c) (2)5 Example 3: Evaluate the expression for the given value of the variables. A) x 2 for x 4 B) 2a 0b4 for a 5 and b 3 Check It Out! Example 3: Evaluate the expression for the given value of the variable. a) p3 for p 4 b) 8a 2b0 for a 2 and b 6 Example 4: Simplify. A) 7w4 B) 5 k 2 C) a 0 b 2 c 3 d 6 b) r 3 7 c) g4 h 6 Check It Out! Example 4: Simplify. a) 2r 0m 3