Divide $4$ by $\frac{4}{\frac{9}{\sqrt{777777}}}$ by multiplying $4$ by the reciprocal of $\frac{4}{\frac{9}{\sqrt{777777}}}$.
$$\frac{4\times \frac{9}{\sqrt{777777}}}{4}$$
Cancel out $4$ and $4$.
$$\frac{9}{\sqrt{777777}}$$
Factor $777777=7^{2}\times 15873$. Rewrite the square root of the product $\sqrt{7^{2}\times 15873}$ as the product of square roots $\sqrt{7^{2}}\sqrt{15873}$. Take the square root of $7^{2}$.
$$\frac{9}{7\sqrt{15873}}$$
Rationalize the denominator of $\frac{9}{7\sqrt{15873}}$ by multiplying numerator and denominator by $\sqrt{15873}$.
