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

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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 $-> sqrta = a^(1/2)$

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

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

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

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

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

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

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

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

$rArr 3x^(1/8)$

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