To raise a power to another power, multiply the exponents. Multiply $2$ and $1$ to get $2$.
$$\frac{1}{2}\sqrt{16^{2}+18^{2}}$$
Calculate $16$ to the power of $2$ and get $256$.
$$\frac{1}{2}\sqrt{256+18^{2}}$$
Calculate $18$ to the power of $2$ and get $324$.
$$\frac{1}{2}\sqrt{256+324}$$
Add $256$ and $324$ to get $580$.
$$\frac{1}{2}\sqrt{580}$$
Factor $580=2^{2}\times 145$. Rewrite the square root of the product $\sqrt{2^{2}\times 145}$ as the product of square roots $\sqrt{2^{2}}\sqrt{145}$. Take the square root of $2^{2}$.
