Explain why rational exponents are not defined when the denominator of the exponent in lowest terms is even and the base is negative

Question

zzr0ck3r · Answer

assume x > 0 then (-x)^(1/2) = sqrt(-x) and we cant take sqaure roots of negative nnumbers.............yet

zzr0ck3r · Answer

so (-3)^(1/4) is $$\sqrt[4]{-3}$$ which is not ok but $$\sqrt[3]{-3}$$ is fine

anonymous · Answer

such square roots are possible in complex number system.....if u'll probably not know  about it if u r learning elementary number theory......but as for real number system such square root s are not possible..

zzr0ck3r · Answer

make sense?

anonymous · Answer

still confused sorry

zzr0ck3r · Answer

what is the square root of -2?

anonymous · Answer

doesnt exist

zzr0ck3r · Answer

what is the 3rd root of -8?

anonymous · Answer

2

zzr0ck3r · Answer

-2 right?

anonymous · Answer

-2

zzr0ck3r · Answer

so you cant take the squared but you can take the qubed root of a negative number right?

anonymous · Answer

right

zzr0ck3r · Answer

in other words (-1)^(1/2) does not have an answer but (-1)^(1/3) does

anonymous · Answer

yes

zzr0ck3r · Answer

extend that and
(-1)^(1/(even number)) has no answer but (-1)^(1/(odd number)) does

zzr0ck3r · Answer

when I say extend that I just mean extend the idea

zzr0ck3r · Answer

(-1)^(1/2) = not ok                  (-1)^(1/3) =  ok
(-1)^(1/4) = not ok                  (-1)^(1/5) = ok
(-1)^(1/6) = not ok                  (-1)^(1/7) =  ok

anonymous · Answer

ok how could you explain this in words?

zzr0ck3r · Answer

we cant take the nth root of a number unless n is odd

zzr0ck3r · Answer

err we cant take the nth root of a negative number unless n is odd

anonymous · Answer

because why?

zzr0ck3r · Answer

because nth roots of a negative number when n is even are undefined such as sqrt(-2)

zzr0ck3r · Answer

because nothing times itself is negative

zzr0ck3r · Answer

a*a is always positive when a is a real number

anonymous · Answer

and thats the explanation?

zzr0ck3r · Answer

we cant take the nth root of a negative number unless n is odd because nth roots of a negative number when n is even are undefined such as sqrt(-2)

zzr0ck3r · Answer

understand it and say it however you want.

zzr0ck3r · Answer

your teacher is not looking for a proof, just wants you to understand the language and the know how.

anonymous · Answer

ok this was very helpful thank you!

zzr0ck3r · Answer

x^(1/2) the 1/2 part is the rational exponent so the denominator is the number we are concerned with.

zzr0ck3r · Answer

aight man i got to sleep goodluck

anonymous · Answer

thank you!!!!

zzr0ck3r · Answer

for sure