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4.4 and 4.5 Fractional and Negative Exponents
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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.
4.4 and 4.5 Fractional and Negative Exponents
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April 24, 2014
Positive Exponents
A positive exponent means that you are multiplying the base that many times...
4.4 and 4.5 Fractional and Negative Exponents
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April 24, 2014
Fractional Exponents
When n is a natural number and x is a rational number,
Example:
4.4 and 4.5 Fractional and Negative Exponents
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April 24, 2014
"Proof"
4.4 and 4.5 Fractional and Negative Exponents
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Examples
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What do we do with a power like this?
Try re-writing the power using one of the other exponent laws...
4.4 and 4.5 Fractional and Negative Exponents
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April 24, 2014
Example: Write the following form in 2 ways:
Example: Write the following in exponent form:
4.4 and 4.5 Fractional and Negative Exponents
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4.4 and 4.5 Fractional and Negative Exponents
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April 24, 2014
4.4 and 4.5 Fractional and Negative Exponents
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REMINDERReciprocals
We know it as..."Bottom becomes top and top becomes bottom"
MathematicallyTwo numbers with a product of 1 are reciprocals
4.4 and 4.5 Fractional and Negative Exponents
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Powers with Negative Exponents
When x is any non-zero number and n is a rational number, x-n is the reciprocal of xn
4.4 and 4.5 Fractional and Negative Exponents
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Apply exponent laws and think about it...
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Example: Evaluate each power:
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We can apply rational exponents and negative exponents together to form a super exponent!!
Does order matter?
4.4 and 4.5 Fractional and Negative Exponents
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April 24, 2014
4.4 and 4.5 Fractional and Negative Exponents
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Example
