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Simplify 2^(x + 3y)*4^(x - y)/sqrt(2*4)

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xetabeta | Student, Kindergarten | Salutatorian

Posted September 10, 2013 at 6:00 AM via web

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Simplify 2^(x + 3y)*4^(x - y)/sqrt(2*4)

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted September 10, 2013 at 6:05 AM (Answer #1)

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The expression `(2^(x + 3y)*4^(x - y))/sqrt(2*4)` has to be simplified.

`(2^(x + 3y)*4^(x - y))/sqrt(2*4)`

= `(2^(x + 3y)*4^(x - y))/8^(1/2)`

= `(2^(x + 3y)*4^(x - y))/2^(3/2)`

= `(2^(x + 3y)*2^(2x - 2y))/2^(3/2)`

use the property `a^x/a^y = a^(x - y)` and `a^x*a^y = a^(x + y)`

= `2^(x + 3y + 2x - 2y - 3/2)`

= `2^(3x + y - 3/2)`

The simplified form of ` (2^(x + 3y)*4^(x - y))/sqrt(2*4) = 2^(3x + y - 3/2)`

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