How do you simplify #\sqrt { ( 729x ^ { \frac { 3} { 4} } ) ^ { \frac { 1} { 3} } }#?

Question

1201 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-09-09T08:24:03

#3x^(1/8)#

#sqrt((729x^(3/4))^(1/3))#

#sqrt((729^(1/3) xx x^(3/4 xx 1/3))#

#sqrt((729^(1/3) xx x^(cancel3/4 xx 1/cancel3))#

#sqrt(729^(1/3) xx x^(1/4))#

#sqrt((27^2)^(1/3) xx x^(1/4))#

#sqrt(27^(2 xx 1/3) xx x^(1/4))#

#sqrt(27^(2/3) xx x^(1/4))#

Recall #-> sqrta = a^(1/2)#

#rarr (27^(2/3) xx x^(1/4))^(1/2)#

#rArr (27^(2/3 xx 1/2) xx x^(1/4 xx 1/2))#

#rArr (27^(cancel2/3 xx 1/cancel2) xx x^(1/8))#

#rArr (27^(1/3) xx x^(1/8))#

#rArr ((3^3)^(1/3) xx x^(1/8))#

#rArr (3^(3 xx 1/3) xx x^(1/8))#

#rArr (3^(cancel3 xx 1/cancel3) xx x^(1/8))#

#rArr (3^1 xx x^(1/8))#

#rArr 3x^(1/8)#