Question

Which expression is equivalent to (16x^8y^-12)1/2

Answer 1

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Answer 2

`(16x^8y^(-12))^(1)/(2)=(4^2x^8y^(-12))^(1)/(2)=(4^2)^(1)/(2)(x^8)^(1)/(2)(y^(-12))^(1)/(2)\\\\=4^{2\cdot(1)/(2)}x^{8\cdot(1)/(2)}y^{-12\cdot(1)/(2)}=4^1x^4y^(-6)=4x^4y^(-6)=(4x^4)/(y^6)\\\\\text{Used:}\\\\(a\cdot b)^n=a^n\cdot b^n\\\\(a^n)^m=a^(n\cdot m)\\\\a^(-n)=(1)/(a^n)`