To multiply powers of the same base, add their exponents. Add $2$ and $1$ to get $3$.
$$\frac{17\times 4^{3}\times 42}{\sqrt{85600}}$$
Calculate $4$ to the power of $3$ and get $64$.
$$\frac{17\times 64\times 42}{\sqrt{85600}}$$
Multiply $17$ and $64$ to get $1088$.
$$\frac{1088\times 42}{\sqrt{85600}}$$
Multiply $1088$ and $42$ to get $45696$.
$$\frac{45696}{\sqrt{85600}}$$
Factor $85600=20^{2}\times 214$. Rewrite the square root of the product $\sqrt{20^{2}\times 214}$ as the product of square roots $\sqrt{20^{2}}\sqrt{214}$. Take the square root of $20^{2}$.
$$\frac{45696}{20\sqrt{214}}$$
Rationalize the denominator of $\frac{45696}{20\sqrt{214}}$ by multiplying numerator and denominator by $\sqrt{214}$.
