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# 4.4 and 4.5 fractional and negative exponents

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### 4.4 and 4.5 fractional and negative exponents

1. 1. 4.4 and 4.5 Fractional and Negative Exponents 1 April 24, 2014 4.5 and 4.6 - Fractional and Negative Exponents Up until now, you have probably only have ever seen exponents as positive integers. Exponents can also be fractional and/or negative, but these have special meanings.
2. 2. 4.4 and 4.5 Fractional and Negative Exponents 2 April 24, 2014 Positive Exponents A positive exponent means that you are multiplying the base that many times...
3. 3. 4.4 and 4.5 Fractional and Negative Exponents 3 April 24, 2014 Fractional Exponents When n is a natural number and x is a rational number, Example:
4. 4. 4.4 and 4.5 Fractional and Negative Exponents 4 April 24, 2014 "Proof"
5. 5. 4.4 and 4.5 Fractional and Negative Exponents 5 April 24, 2014 Examples
6. 6. 4.4 and 4.5 Fractional and Negative Exponents 6 April 24, 2014 What do we do with a power like this? Try re-writing the power using one of the other exponent laws...
7. 7. 4.4 and 4.5 Fractional and Negative Exponents 7 April 24, 2014 Example: Write the following form in 2 ways: Example: Write the following in exponent form:
8. 8. 4.4 and 4.5 Fractional and Negative Exponents 8 April 24, 2014
9. 9. 4.4 and 4.5 Fractional and Negative Exponents 9 April 24, 2014
10. 10. 4.4 and 4.5 Fractional and Negative Exponents 10 April 24, 2014 REMINDER Reciprocals We know it as... "Bottom becomes top and top becomes bottom" Mathematically Two numbers with a product of 1 are reciprocals
11. 11. 4.4 and 4.5 Fractional and Negative Exponents 11 April 24, 2014 Powers with Negative Exponents When x is any non-zero number and n is a rational number, x-n is the reciprocal of xn
12. 12. 4.4 and 4.5 Fractional and Negative Exponents 12 April 24, 2014 Apply exponent laws and think about it...
13. 13. 4.4 and 4.5 Fractional and Negative Exponents 13 April 24, 2014 Example: Evaluate each power:
14. 14. 4.4 and 4.5 Fractional and Negative Exponents 14 April 24, 2014 We can apply rational exponents and negative exponents together to form asuper exponent!! Does order matter?
15. 15. 4.4 and 4.5 Fractional and Negative Exponents 15 April 24, 2014
16. 16. 4.4 and 4.5 Fractional and Negative Exponents 16 April 24, 2014 Example