4.4 and 4.5 fractional and negative exponents

4.4 and 4.5 Fractional and Negative Exponents

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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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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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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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"Proof"

4.4 and 4.5 Fractional and Negative Exponents

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Examples

4.4 and 4.5 Fractional and Negative Exponents

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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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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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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...

4.4 and 4.5 Fractional and Negative Exponents

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Example: Evaluate each power:

4.4 and 4.5 Fractional and Negative Exponents

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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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4.4 and 4.5 Fractional and Negative Exponents

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Example