1. **State the problem:** Simplify the expression $$4^5 \cdot 4^6$$ using the properties of exponents. 2. **Recall the property of exponents:** When multiplying powers with the same base, add the exponents: $$a^m \cdot a^n = a^{m+n}$$ 3. **Apply the property:** Here, the base is 4, so: $$4^5 \cdot 4^6 = 4^{5+6}$$ 4. **Simplify the exponent:** $$4^{5+6} = 4^{11}$$ 5. **Final answer:** $$\boxed{4^{11}}$$ This is the simplified form of the expression.