Question

Which expression is equivalent to (16x^6y^-12)1/2

Answer 1

`(16x^6y^(-12))^(1)/(2)=(4^2x^6y^(-12))^(1)/(2)=(4^2)^(1)/(2)(x^6)^(1)/(2)(y^(-12))^(1)/(2)\\\\=4^{2\cdot(1)/(2)}x^{6\cdot(1)/(2)}y^{-12\cdot(1)/(2)}=4^1x^3y^(-6)=4x^3y^(-6)=(4x^3)/(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)`