Zero & Negative Exponents
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The document discusses zero and negative exponents. It states that for any nonzero number a, a0 = 1. It also states that for any nonzero number a and integer n, a-n = 1/an. Finally, it discusses how to rewrite expressions with negative exponents so that all exponents are positive by moving the base with the negative exponent to the denominator.
Zero & Negative Exponents
- 1. Zero & Negative Exponents 06/01/09 PH 8-4 Bitsy Griffin
- 2. Zero exponent For any nonzero number a, a 0 = 1 5 0 = 1 (-2) 0 = 1 (2/3) 0 = 1 1.02 0 = 1 - 8 0 = -1 06/01/09 PH 8-4 Bitsy Griffin
- 3. Evaluate the function For t = 0 f(t) = 1000 2 t Substitute 0 in for t We know that 2 0 = 1 So the function = 1000 06/01/09 PH 8-4 Bitsy Griffin
- 4. Negative exponents For any nonzero number a and any integer n, a –n = 1/a n Remember that any number (even one with an exponent) is a numerator sitting on top of a denominator. a –n /1 = 1/a n 06/01/09 PH 8-4 Bitsy Griffin
- 5. Negative exponents Writing it on your paper is easier to see because you lose the angle. AND 1/a –n = a n /1 What just happened? Think of the – in front of the exponent as a piece of direction to move the base with the exponent. 06/01/09 PH 8-4 Bitsy Griffin
- 6. Negative exponents As soon as you move it, you drop the negative in front of the exponent. BUT you wouldn’t drop one in front of the base. 1/- a –n = - a n /1 6 –4 = 1/6 4 1/8 –2 = 8 2 06/01/09 PH 8-4 Bitsy Griffin
- 7. Write as a simple fraction 4 –3 1/4 3 1/64 (-3) –2 1/ (-3) 2 1/9 06/01/09 PH 8-4 Bitsy Griffin
- 8. Rewrite each so that all exponents are positive Exponents only go with the variable directly in front of it! 4yx –3 /1 4y(1/x 3 ) 4y/x 3 1/w –4 1 w 4 w 4 06/01/09 PH 8-4 Bitsy Griffin
- 9. Graph the function over the domain -2 ≤ x ≤ 2 Set your calculator margins so that you have an x minimum of -2 and an x maximum of 2. Leave the y at -10 and 10. Sketch each graph as you see it. Pay attention to how each graph differs, and make note of why you think they differ. 06/01/09 PH 8-4 Bitsy Griffin