To multiply powers of the same base, add their exponents. Add $9$ and $-13$ to get $-4$.
$$\sqrt{9\times 10^{-4}\times 9}$$
Calculate $10$ to the power of $-4$ and get $\frac{1}{10000}$.
$$\sqrt{9\times \frac{1}{10000}\times 9}$$
Multiply $9$ and $\frac{1}{10000}$ to get $\frac{9}{10000}$.
$$\sqrt{\frac{9}{10000}\times 9}$$
Multiply $\frac{9}{10000}$ and $9$ to get $\frac{81}{10000}$.
$$\sqrt{\frac{81}{10000}}$$
Rewrite the square root of the division $\frac{81}{10000}$ as the division of square roots $\frac{\sqrt{81}}{\sqrt{10000}}$. Take the square root of both numerator and denominator.
