Question

What expression is equivalent to [x1/4*y16]^1/2

Answer 1

Answer:

The given expression is ${{{\bf x}^{\frac{\bf 1}{\bf 4}}\times y^{\bf 16}}} ^ {\frac{1}{2}} =x^{\frac {\bf 1}{\bf 8}}\times y^{\bf 4}$.

Step-by-step explanation:

The given expression is ${{x^{\frac{1}{4}}\times y^{16}}}^\frac{1}{2}$

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

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

${{x^{\frac{1}{4}}\times y^{16}}}^{\frac{1}{2}}=x^{\frac{1}{4}}^\frac{1}{2}} \times y^{4}$

${{x^{\frac{1}{4}}\times y^{16}}}^{\frac{1}{2}}= x^{\frac{1}{8}}\times y^{4}$  by using ${a^{m}} ^{n}=a^ {mn}$ property.