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Evaluating fractional exponents: negative unit-fraction

CCSS.Math: ,

Video transcript

let's do some slightly more complicated fractional exponent examples so we already know that if I were to take 9 to the 1/2 power this is going to be equal to 3 and we know that because 3 times 3 is equal to 9 this is equivalent to saying what is the principal root of 9 well that is equal to 3 but what would happen if I took a 9 to the negative 1/2 power now we have a negative fractional exponent and the key to this is to just not get too not to get too worried or intimidated by this but just think about it step by step just ignore for the second that this is a fraction and just look at this negative first just breathe slowly and realize okay I got a negative negative exponent that means that this is just going to be 1 over 9 to the 1/2 that's what that negative is the cue for this is 1 over 9 to the 1/2 and we know that 1 to the 9 to the 1/2 is equal to 3 so this is just going to be equal to 1 this is just going to be equal to 1/3 let's take things a little bit further what would have what would this evaluate to and I encourage you to pause the video after trying it or pause the video to tried negative 27 negative 27 to the negative 1/3 power so I encourage you to pause the video and think about what this would evaluate to so remember just take a deep breath you can always get rid of this negative in the exponent by taking the reciprocal and raising it to the positive so this is going to be equal to 1 over negative 27 to the positive 1/3 power and I know what you're saying hey I still can't breathe easily I have this negative number to this fractional exponent but this is just saying what number if I were to multiply it three times if I multiple so if I have that number so whatever the number this is I were to multiply it I took three of them and I multiplied them together if I multiplied one by that number three times what number what would I have to use here to get negative 27 well we already know we already know that 3 to the third which is equal to 3 times 3 times 3 is equal to positive 27 so that's a pretty good clue what would negative 3 to the third power be well that's negative 3 times negative 3 times negative 3 which is negative 3 times negative 3 is positive 9 times negative 3 is negative 27 so we just found this number this question mark negative 3 times negative 3 times negative 3 is equal to negative 27 so negative 27 to the 1/3 this part right over here is equal to negative 3 so this is going to be equal to 1 1 over 1 over negative 3 which is the same thing as negative as negative 1/3