Simplify \(\sqrt[4]{256a^2b^4}\).

\(\color{green}\boxed{{\color{navy}x}~{\color{lightblue}x}^{\color{navy}y}~{\color{black}\frac{\color{navy}x}{\color{navy}y}}~\color{black}\sqrt{\color{navy}x}~~{\color{navy}+~~-~\times}}\)

\(\color{red}\boxed{{\color{black}\sqrt[\color{navy}y]{\color{lightblue}x}}}\)

SpaceModo
Jan 26, 2018

#1**0 **

4 x 4 x 4 x 4 = 256

=4ba^(1/2)

I do not know what the rest of your question means.....

ElectricPavlov
Jan 26, 2018

#2**+2 **

I beg to differ just a little EP

By convention the answer must be positive and we do not know if a or b is pos or neg.

\(\sqrt[4]{256a^2b^4}\\ =\sqrt[2]{16|a|b^2}\\ =4\sqrt{|a|}|b|\\ =|\;4b\sqrt{|a|}\;|\\ or\\ =|\;4b|a|^{1/2}\;|\\\)

Melody
Jan 27, 2018

#3**+1 **

Agree ! Melody is correct.... ! I was thinking about a^2 and b^4 both being POSITIVE results...but that does not tell us if a or b are positive themselves !

ElectricPavlov
Jan 28, 2018