which expression is equivalent to (x^1/4 y ^16)^1/2

Answer:Equivalent expression is [tex]x^{\frac{1}{8}}y^{8}[/tex]Step-by-step explanation:Given Expression is [tex](x^{\frac{1}{4}}y^{16})^{\frac{1}{2}}[/tex]We have to find Equivalent expression to given expression.using law of exponent , [tex](ab)^x=a^xb^x[/tex]we get,[tex]\implies(x^{\frac{1}{4}})^{\frac{1}{2}}(y^{16})^{\frac{1}{2}}[/tex]now using another law of exponent, [tex](x^a)^b=x^{ab}[/tex]we get,[tex]\implies x^{\frac{1}{4}\times\frac{1}{2}}y^{16\times\frac{1}{2}}[/tex][tex]\implies x^{\frac{1}{8}}y^{8}[/tex]Therefore, Equivalent expression is [tex]x^{\frac{1}{8}}y^{8}[/tex]