I am a bit confused at the concept of fractional exponents. I understand that 8 ^ (2/3) is equal to the third root of (8^2) = 4; another way of doing this is taking the third root of 8 then taking that total and squaring it = 4.
Using the same approaches used above why does √[(-5) ^2] = 5 and (√-5) ^ 2 = undefined?
Why are there contradictory results here when we are using basic properties of fractional exponents?
Also, how is √[(-5)^2] = 5? Shouldn't it be equal to (-5) ^ (2/2) = -5? I used (2/2) because the exponent that the base is raised to is 2, and the root is 2.
Last but not least, why is (-5) ^ (2/2) = -5? Using the properties why can't it be equal to √[(-5) ^2] = 5, or (√-5) ^ 2 = undefined?
I know some of these questions may seem redundant but I am just trying to master this concept. Thank you guys so much for your feedback!
Using the same approaches used above why does √[(-5) ^2] = 5 and (√-5) ^ 2 = undefined?
Why are there contradictory results here when we are using basic properties of fractional exponents?
Also, how is √[(-5)^2] = 5? Shouldn't it be equal to (-5) ^ (2/2) = -5? I used (2/2) because the exponent that the base is raised to is 2, and the root is 2.
Last but not least, why is (-5) ^ (2/2) = -5? Using the properties why can't it be equal to √[(-5) ^2] = 5, or (√-5) ^ 2 = undefined?
I know some of these questions may seem redundant but I am just trying to master this concept. Thank you guys so much for your feedback!
