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Simplify:  `root(8)(16x^12)^6` ` `

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kristenmarieb... | Student, Grade 10 | Valedictorian

Posted April 22, 2013 at 5:31 AM via web

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Simplify:

 `root(8)(16x^12)^6`

` `

2 Answers | Add Yours

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted April 22, 2013 at 5:46 AM (Answer #1)

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The expression `(root(8) (16x^12))^6` has to be simplified.

`(root(8) (16x^12))^6`

= `(16x^12)^(6/8)`

= `16^(3/4)*(x^12)^(3/4)`

= `(2^4)^(3/4)*x^(12*(3/4))`

= `2^3*x^9`

= `8*x^9`

The expression `(root(8) (16x^12))^6 = 8*x^9`

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oldnick | Valedictorian

Posted April 22, 2013 at 4:55 PM (Answer #2)

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`(root(8)(16x^12))^6=root(8)(2^24)root(8)(x^72)=2^3x^9=8x^9`

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