1. **State the problem:** Simplify the expression $$\frac{2^3 \times 2^2}{3^4}$$. 2. **Recall the laws of exponents:** When multiplying powers with the same base, add the exponents: $$a^m \times a^n = a^{m+n}$$. 3. **Apply the rule to the numerator:** $$2^3 \times 2^2 = 2^{3+2} = 2^5$$. 4. **Rewrite the expression:** $$\frac{2^5}{3^4}$$. 5. **Calculate the powers:** $$2^5 = 32$$ and $$3^4 = 81$$. 6. **Final simplified fraction:** $$\frac{32}{81}$$. This fraction cannot be simplified further because 32 and 81 have no common factors other than 1. **Answer:** $$\frac{32}{81}$$.