Final answer:
The expression (2*6)³÷² simplifies to 216 by first applying the power to both 2 and 6, and then recognizing that 8 divided by 2³ (which is also 8) results in 1, leaving 216 as the final answer.
Step-by-step explanation:
The question requires the simplification of the expression (2×6)³÷² using properties of rational exponents. To simplify, we can use the exponentiation rules for products. When raising a product to a power, the power distributes over the factors. Therefore, (2×6)³ = 2³×6³. Now, the full expression is (2³×6³)÷².
When dividing powers with the same base, we subtract the exponents. Since 2³ = 8 and 6³ = 216, the expression simplifies to 8×216÷² = 8×216÷(2³). Then, subtracting the exponents for the terms involving 2 yields: 8÷(2³)×216 = 2°×216 = 1×216, which simplifies to 216.