Question 8125: An answer in my Algebra book contains the following exponential notation:
(-1/2)^9. This is shown as equaling (-1/2^9). I am familiar with exponential notation that has integers with fractional exponents but I do not know how this negative fraction with the interger exponent outisde of the parenthesis becomes minus 1/2 with the 9 now the exponent over the 2 in the denominator within the parenthesis. So, how does (-1/2)^9 become (-1/2^9)?
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Think about this:
(-1/2)^9 = (-1/2)*(-1/2)*...*(-1/2) = -.001953125...
Each time you multiply (-1/2) by itself, the sign changes from negative to positive. And the next iteration, the sign becomes negative again. So, if you do this an odd number of times (9), the end result will have a negative sign.
(-1/2^9) = -(1/2^9) = -((1/2)*(1/2)*(1/2)*...*(1/2)) = -(.001953125...) = -.001953125...
In this case, the negative sign applies to the end result.
So, the bottom line is: (-1/2)^9 = (-1/2^9), but this would not be the case if the exponent were an even integer.
(-1/2^8) = -.00390625...
(-1/2)^8 = .00390625...
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