Question

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

Answer 1

$(16x^6y^{-12})^\frac{1}{2}=(4^2x^6y^{-12})^\frac{1}{2}=(4^2)^\frac{1}{2}(x^6)^\frac{1}{2}(y^{-12})^\frac{1}{2}\\\\=4^{2\cdot\frac{1}{2}}x^{6\cdot\frac{1}{2}}y^{-12\cdot\frac{1}{2}}=4^1x^3y^{-6}=4x^3y^{-6}=\dfrac{4x^3}{y^6}\\\\\text{Used:}\\\\(a\cdot b)^n=a^n\cdot b^n\\\\(a^n)^m=a^{n\cdot m}\\\\a^{-n}=\dfrac{1}{a^n}$