The given expression simplifies to $\frac{27}{16}$.

Would you like further explanation or have any questions? Here are some related problems for further practice:

1. Simplify $\frac{2^3 \cdot 2^{-1}}{2^2}$.
2. Evaluate $\frac{5^0 \cdot 5^3 \cdot 10^{-2}}{5^{-1} \cdot 10^1}$.
3. Simplify $\frac{x^4 \cdot x^{-3}}{x^{-1}}$.
4. Solve $\frac{7^0 \cdot 7^2 \cdot 9^{-3}}{7^{-1} \cdot 9^{-2}}$.
5. Simplify $\frac{(2a^3b^{-2})}{a^{-1}b^0}$.

Tip: When dividing or multiplying powers with the same base, remember to add or subtract the exponents!