Use the rules of exponents to simplify the expression.
$$\sqrt{\sqrt[7]{16}}$$
To raise a power to another power, multiply the exponents.
$$16^{\frac{1}{7}\times \frac{1}{2}}$$
Multiply $\frac{1}{7}$ times $\frac{1}{2}$ by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.