Question

PLEASE HELP!!!!

How do I write -8^(4/5), as a rational exponent?

Answer 1

it is a rational exponent

Answer 2

I know, but I need it to be further simplified, if it can.

Answer 3

Actually, I got it out of a radical - I'm going from radical from, to rational exponent form.

Answer 4

actually i am wrong, you would write
\[-\sqrt[5]{8^4}\] you cannot do anything else

Answer 5

Oh, okay - so -8^(4/5) cannot be simplified any more?

Answer 6

I thought, where there is a negative 8, I would make it into a fraction.

Answer 7

hold on

\[\sqrt[n]{x^m}\] is radical form
\[x^{\frac{m}{n}}\] is exponential form
you have it in exponential form
you do not know what the fifth root of 8 is (the cube root is 2) so you cannot simplify this further. your exponent is \(\frac{4}{5}\) and you cannot reduce this fraction, so you are done

Answer 8

OH, I see! Okay, that makes sense. Thank you very much! :)

Answer 9

also don't be confused about the minus sign.
if it was in the EXPONENT that would mean take the reciprocal
for example
\[8^{-\frac{1}{3}}=\frac{1}{2}\] but the minus sign out front just means make it negative

Answer 10

yw

Answer 11

OH, I see! That makes a lot of sense. I always get confused over whether or not it's the exponent or the base that turns it into a fraction.

Answer 12

only if the minus sign is in the exponent do you take the reciprocal
actually you already know this because i am sure you do not believe that \(-2=\frac{1}{2}\)

Answer 13

Ha, ha - yes, that's true! :) Thanks!