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September 10, 2015 Essential Question: 1. How do you use zero and negative exponents? 2. How do you find cube roots? Videos: What do you do with a negative exponent? What do you do with a zero exponent? How will you see this on the Keystone Exam? Simplify: 2(2√4)-2 a. 1/8 How do you simplify an expression with negative exponents? b. 1/4 c. 16 d. 32 New Rules.... New Stuff.....Definition of Zero Exponent Any negative number raised to an even power will be _____ Ex. (-2) (-3) 2 (-1) 4 (-4) 6 (-2) 2 6 Any negative number raised to an odd power will be ______ In words: a to the zero power is 1 (when a ≠ 0) Algebra: a0 = 1 Examples: 50 = 1 Be Careful: 00 = undefined 3 (-3) 5 (-1) 9 (-4) 3 (-2) 3 x0 = 1 (4x4y18)0 = 1 More Examples: 4x5y12z130 Ex. (-2) How do you evaluate negative exponents? 0 vs. 4x5y0z130 2 September 10, 2015 New Stuff.....Definition of Negative Exponents In words: a-n is the reciprocal of an when a ≠ 0 1 Backwards: 1-n = an Algebra: a-n = an a Example: 2-1 = 1 21 Example: Examples..... Problem Write answer using only positive exponents. Always simplify. x4y-2 1 = 31 3-1 (x2y-1)-1 How does this work with variables? Answer: Just take the variable to the opposite "level" and make exponent positive. 3 10 -9 -3 -5 x y7 x y-7 xy z a-2v-5w10 Simplify...write your answers using only positive exponents. (2x)-3y5 x5y-2 Examples with numbers.... Problem (x-4y3)-5 23 x3y-2z0 x-4y8 (3x-2y5)-2 2-3 (-4)-2 Rewrite with positive exponents..........then evaluate September 10, 2015 Examples..... Problem Evaluate....(ie. write the answer w/o exponents) Write with positive exponents..................Then evaluate 2 -1 5 ( ( 5-2 (( 4-1 43 1 3-2 3-2 3-5 8 9 -2 Be Careful.....what does your negative exponent "touch" ? Back to zeros.....Examples..... Problem (3x ) 5 -4 3(x5)-4 3x-5 Evaluate Think..... 04 Think..... 40 Think..... 0-3 September 10, 2015 Video: Simplifying a cube root Cube root of a non-perfect cube. Practice: Cube roots