1. **State the problem:** Write the product $8 \cdot 2 \cdot 2 \cdot 4 \cdot 4 \cdot 4$ using exponential notation. 2. **Understand exponential notation:** Exponential notation expresses repeated multiplication of the same number as $a^n$, where $a$ is the base and $n$ is the exponent (how many times $a$ is multiplied by itself). 3. **Factor each number into primes:** - $8 = 2^3$ - $2 = 2^1$ - $4 = 2^2$ 4. **Rewrite the product using prime factors:** $$8 \cdot 2 \cdot 2 \cdot 4 \cdot 4 \cdot 4 = 2^3 \cdot 2^1 \cdot 2^1 \cdot 2^2 \cdot 2^2 \cdot 2^2$$ 5. **Use the rule of exponents for multiplication:** When multiplying powers with the same base, add the exponents: $$a^m \cdot a^n = a^{m+n}$$ 6. **Add all exponents:** $$3 + 1 + 1 + 2 + 2 + 2 = 11$$ 7. **Final exponential notation:** $$2^{11}$$ **Answer:** $8 \cdot 2 \cdot 2 \cdot 4 \cdot 4 \cdot 4 = 2^{11}$