1. **State the problem:** Calculate the value of the expression $3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 9$. 2. **Rewrite the expression using exponents:** Since $3$ is multiplied by itself $8$ times, we can write this as $3^8 \times 9$. 3. **Express 9 as a power of 3:** Note that $9 = 3^2$, so the expression becomes $3^8 \times 3^2$. 4. **Use the exponent multiplication rule:** When multiplying powers with the same base, add the exponents: $3^8 \times 3^2 = 3^{8+2} = 3^{10}$. 5. **Calculate $3^{10}$:** $$3^{10} = 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 = 59049$$ **Final answer:** $59049$