1. **State the problem:** Simplify each of the following expressions involving powers of 3: a) $3^4 \cdot 3^3$ b) $3^4 \cdot 3^{-3}$ c) $\frac{3^3}{3^4}$ d) $(3^4)^3$ 2. **Recall the exponent rules:** - Product of powers: $a^m \cdot a^n = a^{m+n}$ - Power of a power: $(a^m)^n = a^{m \cdot n}$ - Quotient of powers: $\frac{a^m}{a^n} = a^{m-n}$ 3. **Simplify each expression step-by-step:** a) $3^4 \cdot 3^3 = 3^{4+3} = 3^7$ b) $3^4 \cdot 3^{-3} = 3^{4 + (-3)} = 3^{1} = 3$ c) $\frac{3^3}{3^4} = 3^{3-4} = 3^{-1} = \frac{1}{3}$ d) $(3^4)^3 = 3^{4 \cdot 3} = 3^{12}$ 4. **Final answers:** a) $3^7$ b) $3$ c) $\frac{1}{3}$ d) $3^{12}$