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Simplify.  A) (x/2m^4)^7 B) (5x/7y^2)^2

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Simplify.  A) (x/2m^4)^7 B) (5x/7y^2)^2

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mjripalda's profile pic

Posted (Answer #1)

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To simplify these expressions, apply these three properties of exponents which are:

`(a/b)^m=a^m/b^m `  ,    `(ab)^m=a^mb^m`     and     `(a^m)^n=a^(m*n)` .

(A)

`(x/(2m^4))^7=x^7/(2m^4)^7=x^7/(2^7(m^4)^7)`

`=x^7/(2^7m^(4*7))=x^7/(2^7m^28)=x^7/(128m^28)`

(B)

`((5x)/(7y^2))^2=(5x)^2/(7y^2)^2=(5^2x^2)/(7^2(y^2)^2)`

`=(5^2x^2)/(7^2y^(2*2))=(5^2x^2)/(7^2y^4)=(25x^2)/(49y^4)`

 

Hence,  `(x/(2m^4))^7=x^7/(128m^28) `    and   `((5x)/(7y^2))^2=(25x^2)/(49y^4)` .

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Posted (Answer #2)

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`A)(x/(2m^4))^7=x^7/(2m^4)^7=x^7/(2^7(m^4)^7)=x^7/(128m^28)`

`B) ((5x)/(7y^2))^2=(5x)^2/(7y^2)^2=(5^2x^2)/(7^2(y^2)^2)=(25x^2)/(49y^4)`

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