which expression is equivalent to $(16x^{8}y^{-12})^{\frac{1}{2}}$?\n- $-4x^{4}y^{6}$\n- $-8x^{4}y^{6}$\n…

Answer:

C. $\frac{4x^{4}}{y^{6}}$

Explanation:

Step1: Apply power - of - a - product rule

$(16x^{8}y^{- 12})^{\frac{1}{2}}=16^{\frac{1}{2}}(x^{8})^{\frac{1}{2}}(y^{-12})^{\frac{1}{2}}$

Step2: Calculate $16^{\frac{1}{2}}$

$16^{\frac{1}{2}}=\sqrt{16}=4$

Step3: Apply power - of - a - power rule for $x$ and $y$ terms

$(x^{8})^{\frac{1}{2}}=x^{8\times\frac{1}{2}} = x^{4}$; $(y^{-12})^{\frac{1}{2}}=y^{-12\times\frac{1}{2}}=y^{-6}=\frac{1}{y^{6}}$

Step4: Combine the results

$4x^{4}\times\frac{1}{y^{6}}=\frac{4x^{4}}{y^{6}}$