#### Answer

$$\frac{3a^{10}c^7}{4}$$

#### Work Step by Step

We know the following rules of exponents.
$$ (1) \ a^m\cdot a^n = a^{m+n} \\ (2) \ (ab)^m =a^mb^m \\ (3) \ (a^m)^n =a^{mn} \\ (4)
\ a^{-m} = \frac{1}{a^m} \\ (5)\ \frac{a^m}{a^n} =a^{m-n} \\ (6) \ a^0=1 \\ (7) \ (\frac{a}{b})^m =\frac{a^m}{b^m}$$
Thus, we find:
$$ \frac{18a^5bc^{10}}{24a^{-5}bc^3}\\ \frac{3a^{10}c^{10-3}}{4}\\ \frac{3a^{10}c^7}{4}$$