| Lesson
Page
Math B
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Use of Positive, Negative
and Zero Exponents |
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In the past, you have been using
positive numbers for powers in your algebraic expressions.
As you may have seen, any integer,
whether positive or negative may be used as an exponent. Even '0' is a valid
exponent, as well as rational numbers (fractions). |
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Remember the rule for dividing
like variables raised to a power?
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Look at the problem
at the right.
==>
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| If we subtract the exponents, we get: |
If we simply 'cancel' like terms: |
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Obviously
equal answers !!!!! |
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What if the problem were
upside down? ==>
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| If we subtract the exponents, we get: |
If we cancel, we get: |
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Not as
obvious, but indeed EQUAL answers !!!!! |
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So, in general, the rule is:  |
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For
example:
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Remember:
an
expression with a negative power ends up on the
opposite side of the fraction bar with a positive power. |
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A Zero
exponent is investigated in much the same way. Examine:
==>
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| If we subtract the exponents, we get: |
If we cancel, we get: |
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Also EQUAL
Answers!!!!
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So,  ,
as long as  . |
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(The above rule is based on division, and we cannot divide by a zero
quantity.
This is why we add the condition to this rule that
.)
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In problems where you have negative
and zero exponents,
simplify whenever possible by using the above rules.
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Check out these problems, and
see if you can follow the steps. |
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Example 1.
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| Solution:
(Remember, anything to the '0' power has a value of
'1'.)
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Example 2.
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| Solution:
(In this case, we introduce the negative power to
move the y variable to the numerator.)
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Example 3.
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| Solution:
(The 2 raised to the negative power moves to the
numerator
with a positive power.) |
Now you are ready to practice your POWERS.
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