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Simplify. (y^x times y^-x)^4

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kristenmarieb... | Student, Grade 10 | (Level 1) Valedictorian

Posted March 23, 2013 at 7:21 PM via web

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Simplify.

(y^x times y^-x)^4

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted March 23, 2013 at 7:29 PM (Answer #1)

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You need to use the exponential laws, that helps you to evaluate the given exponential expression``, such that:

`y^x*y^(-x) = y^(x + (-x)) => y^x*y^(-x) = y^0 => y^x*y^(-x) = 1`

Raising to 4th power, yields:

`(y^x*y^(-x))^4 = 1^4 => (y^x*y^(-x))^4 = 1`

Hence, performing the indicated operations, using the exponentials laws, yields `(y^x*y^(-x))^4 = 1` .

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pramodpandey | College Teacher | (Level 3) Valedictorian

Posted March 24, 2013 at 8:07 AM (Answer #2)

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we know this law of exponent.

`x^m xx x^n=x^(m+n) , `

`x^0=1 `  

So and " times mean multiply "

`(y^x xx y^-x)^4=(y^(x-x))^4`

`=(y^0)^4`

`=1^4`

`=1`

 

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