refresher topic
From working with the rules of exponents (when x is not 0), we know that:
exr2

can be interpreted
as

exr3
which
illustrates
exr4

When the value of a is smaller than the value of b, we arrive at the rule for a negative exponent.

exr5

can be interpreted
as

exr6
which
illustrates
exr7
Remember, an expression with a negative power is moved to the oppostite side of the fraction bar as a positive power.

Should the values of a and b be the same, we have the rule for a zero exponent.
exr8

can be interpreted
as

exr9
which
illustrates
exr10

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expin1
exrp1
 
 

Remember that any value raised to the 0 power is 1. Notice that the zero power affects the entire parentheses which is raised to that power.
expr1a



expin2
exrp2
 
  The 2 raised to the negative power moves to the numerator with a positive power.
Notice that the 0 power only affects the 8 to which it is attached. It does not affect the multiple of 8.
exrp2a



expin3 exrp3
 

Negative exponents will be used to eliminate the denominator.exrp3b



expin4 exrp4
 

Notice how the power of -2 affects both the 3 and the x in the parentheses. If a power is outside a set of parentheses, it affects all of the factors within the parentheses. If there are no parentheses, the power affects only the value to which is it attached.
exrp4b


expin5 exrp5
  In this problem, it will be easier to simplify inside the parentheses first. Did you notice how the last step shows the negative powers expressed as positive powers on the opposite side of the fraction bar?
exrp5a


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