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Simplify the expression. Assume all variables are positive. ( 3sqrt x times sqrt x^5...

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draw | Student, Grade 9 | eNotes Newbie

Posted March 5, 2012 at 7:37 AM via web

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Simplify the expression. Assume all variables are positive.

( 3sqrt x times sqrt x^5 )/sqrt(25x^16)

the 3 is in the root. sqrt stands for the square root sign. x is variable.

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted March 5, 2012 at 8:04 AM (Answer #1)

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`(^3sqrt(x) sqrt(x^5))/sqrt(25x^16) `

`(x^(1/3)(x^(5/2)))/(5x^8)`

`x^(1/3+5/2) / (5x^8)`

`==> (x^(17/6))/(5x^8)`

`==> (1/5) x^(17/6 - 8)`

`==> (1/5)x^(-31/6)`

`==> 1/(5x^(31/6))`

`==> 1/(5 x^(30/6) x^(1/6))`

`==> 1/(5x^5 x^(1/6))`

`==> 1/(5x^5 (^6sqrt x))`

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