Properties of Exponents (MAT306).notebook
October 03, 2014
Negative Exponents
What is another way to write ?
We can think of
as
.
And we know that we subtract exponents
when we divide powers having the same
base.
So...
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Properties of Exponents (MAT306).notebook
October 03, 2014
But
So
Which means...
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Properties of Exponents (MAT306).notebook
Can we write
October 03, 2014
another way?
Are you noticing a pattern?
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Properties of Exponents (MAT306).notebook
October 03, 2014
A negative exponent on a base turns into a
fraction, with the power on the other side
and the sign of the exponent changes to
positive.
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Properties of Exponents (MAT306).notebook
Examples:
October 03, 2014
1)
2)
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Properties of Exponents (MAT306).notebook
October 03, 2014
Notice anything?
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Properties of Exponents (MAT306).notebook
October 03, 2014
When you have a fraction raised to a
negative exponent, flip the fraction, and
change the sign of the exponent.
Example:
Use rule of
power of a
quotient
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Properties of Exponents (MAT306).notebook
October 03, 2014
The "Elevator Rule"
- When powers with negative exponents
appear in a fraction
Move the powers with negative exponents
to the other side of the fraction and change
the signs of their exponents.
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Properties of Exponents (MAT306).notebook
October 03, 2014
Note that only the powers with
negative exponents move.
Don't move anything else!
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Properties of Exponents (MAT306).notebook
October 03, 2014
Rational (Fractional) Exponents
Example:
and
So
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Properties of Exponents (MAT306).notebook
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Example:
and
So
Example:
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Properties of Exponents (MAT306).notebook
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What do you think...
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Properties of Exponents (MAT306).notebook
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A rational exponent turns into a root,
where the denominator of the fraction is
the index of the root.
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Properties of Exponents (MAT306).notebook
October 03, 2014
Question: Can you come up with a rule for
a rational exponent like...
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Properties of Exponents (MAT306).notebook
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