You need to use these two rules of exponents:
To raise a product to a power, raise each factor to the power.
To raise a power to a power, multiply the powers.
The product inside the parentheses is being raised to the power 1/2.
Raise each factor to the power 1/2.
[tex] \left( x^{ \frac{1}{4} } y^{16} \right) ^{\frac{1}{2}} =[/tex]
[tex] = \left( x^{ \frac{1}{4} } \right)^{\frac{1}{2}} \left( y^{16} \right) ^{\frac{1}{2}} [/tex]
Now multiply the exponents.
[tex] = x^{ \frac{1}{8} } y^{8} [/tex]
Finally, use the definition of a rational exponent to change the exponent of x into a root.
[tex]= (\sqrt[8]{x}) y^{8} [/tex]
