1. The problem is to compare the values of the expressions $6^9$, $2^{10}$, $8^9$, and $2^{11}$. 2. We use the property of exponents that allows expressing numbers as powers of prime bases to compare more easily. 3. Express $6^9$ as $(2 \times 3)^9 = 2^9 \times 3^9$. 4. Express $8^9$ as $(2^3)^9 = 2^{27}$. 5. We already have $2^{10}$ and $2^{11}$. 6. Now compare the powers of 2 and 3: - $6^9 = 2^9 \times 3^9$ - $2^{10}$ - $8^9 = 2^{27}$ - $2^{11}$ 7. Since $3^9$ is a large number, $6^9$ is larger than $2^{10}$ and $2^{11}$. 8. $8^9 = 2^{27}$ is the largest because $27 > 9, 10, 11$. Final order from smallest to largest: $2^{10} < 2^{11} < 6^9 < 8^9$.