To multiply powers of the same base, add their exponents. Add $1$ and $2$ to get $3$.
$$\left(1^{3}\times 335^{2}\right)^{22}$$
Calculate $1$ to the power of $3$ and get $1$.
$$\left(1\times 335^{2}\right)^{22}$$
Calculate $335$ to the power of $2$ and get $112225$.
$$\left(1\times 112225\right)^{22}$$
Multiply $1$ and $112225$ to get $112225$.
$$112225^{22}$$
Calculate $112225$ to the power of $22$ and get $1264653381563784308464576671172679726657311918115512301787119385219923854714206305516199790872633457183837890625$.