1. The problem is to find the quotient rule for $6$ raised to the power of $4$. 2. The quotient rule in exponents states that for any nonzero base $a$ and integers $m$ and $n$, $$\frac{a^m}{a^n} = a^{m-n}$$ This means when dividing powers with the same base, subtract the exponents. 3. Here, we only have $6^4$, which is a power, not a quotient of powers, so the quotient rule does not directly apply. 4. However, if you meant to evaluate $6^4$, then: $$6^4 = 6 \times 6 \times 6 \times 6$$ 5. Calculate step-by-step: $$6 \times 6 = 36$$ $$36 \times 6 = 216$$ $$216 \times 6 = 1296$$ 6. Therefore, the value of $6^4$ is $1296$. 7. If you want to apply the quotient rule to an expression like $\frac{6^m}{6^n}$, remember to subtract exponents: $6^{m-n}$. Final answer: $6^4 = 1296$