Question

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

Answer 1

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

Answer 2

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

Answer 3

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..

Answer 4

make sense?

Answer 5

still confused sorry

Answer 6

what is the square root of -2?

Answer 7

doesnt exist

Answer 8

what is the 3rd root of -8?

Answer 9

2

Answer 10

-2 right?

Answer 11

-2

Answer 12

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

Answer 13

right

Answer 14

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

Answer 15

yes

Answer 16

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

Answer 17

when I say extend that I just mean extend the idea

Answer 18

(-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

Answer 19

ok how could you explain this in words?

Answer 20

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

Answer 21

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

Answer 22

because why?

Answer 23

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

Answer 24

because nothing times itself is negative

Answer 25

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

Answer 26

and thats the explanation?

Answer 27

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)

Answer 28

understand it and say it however you want.

Answer 29

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

Answer 30

ok this was very helpful thank you!

Answer 31

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

Answer 32

aight man i got to sleep goodluck

Answer 33

thank you!!!!

Answer 34

for sure