which expression is equivalent to $left(x^{\frac{1}{4}}y^{16}\right)^{\frac{1}{2}}$?\n$x^{\frac{1}{2}}y^{4}$\…

Explanation:

Step1: Apply power - of - a - product rule

According to the rule ((ab)^n=a^n b^n), we have (\left(x^{\frac{1}{4}}y^{16}\right)^{\frac{1}{2}}=(x^{\frac{1}{4}})^{\frac{1}{2}}(y^{16})^{\frac{1}{2}}).

Step2: Apply power - of - a - power rule

The power - of - a - power rule ((a^m)^n=a^{mn}). For ((x^{\frac{1}{4}})^{\frac{1}{2}}), we get (x^{\frac{1}{4}\times\frac{1}{2}} = x^{\frac{1}{8}}). For ((y^{16})^{\frac{1}{2}}), we get (y^{16\times\frac{1}{2}}=y^{8}). So (\left(x^{\frac{1}{4}}y^{16}\right)^{\frac{1}{2}}=x^{\frac{1}{8}}y^{8}).

Answer:

(x^{\frac{1}{8}}y^{8}) (corresponding to the second option in the multiple - choice list)