Answer:
The given expression is [tex]{{{\bf x}^{\frac{\bf 1}{\bf 4}}\times y^{\bf 16}}} ^ {\frac{1}{2}} =x^{\frac {\bf 1}{\bf 8}}\times y^{\bf 4}[/tex].
Step-by-step explanation:
The given expression is [tex]{{x^{\frac{1}{4}}\times y^{16}}}^\frac{1}{2}[/tex]
[tex]{{x^{\frac{1}{4}}\times y^{16}}}^{\frac{1}{2}}=\sqrt{x^{\frac{1}{4}}\times y^{16}}[/tex]
[tex]{{x^{\frac{1}{4}}\times y^{16}}}^{\frac{1}{2}}= \sqrt{x^{\frac{1}{4}}}\times \sqrt{y^{16}}[/tex]
[tex]{{x^{\frac{1}{4}}\times y^{16}}}^{\frac{1}{2}}=x^{\frac{1}{4}}^\frac{1}{2}} \times y^{4}[/tex]
[tex]{{x^{\frac{1}{4}}\times y^{16}}}^{\frac{1}{2}}= x^{\frac{1}{8}}\times y^{4}[/tex] by using [tex]{a^{m}} ^{n}=a^ {mn}[/tex] property.
