 Positive, Negative, & Zero Exponents MathBitsNotebook.com Terms of Use   Contact Person: Donna Roberts  From working with the rules of exponents (when x is not 0), we know that: can be interpreted as which illustrates When the value of a is smaller than the value of b, we arrive at the rule for a negative exponent. can be interpreted as which illustrates 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. can be interpreted as which illustrates    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.   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.   Negative exponents will be used to eliminate the denominator.   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.   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?  