Final answer:
Raising -2 to the sixth power results in 64, which is greater than 24; therefore, the correct operator for (-2)⁶ __ 24 is '>'.
Step-by-step explanation:
To solve the exponential expression (-2)⁶, we must calculate the result of raising -2 to the power of 6. Since any negative number raised to an even exponent results in a positive value, (-2)⁶ would yield 64, because -2 * -2 * -2 * -2 * -2 * -2 equals 64. Comparing 64 with 24, we see that 64 is indeed greater than 24. Thus, the correct operator for the expression (-2)⁶ __ 24 is >.