Select the number that completes the analogy. Perform each operation on the complete number.

6 : 1296 :: 10 : 2160 :: 8 : ?

The correct answer is 1728.

Step-by-step Explanation:

To solve this analogy, we need to determine the operation or relationship applied to the first number to obtain the second number in each given pair.

Analyzing Pair 1 (6 : 1296):

Let us find the ratio between 1296 and 6 by dividing 1296 by 6:

$1296÷6=216$

This shows that the second number is obtained by multiplying the first number by 216:

$6\times 216=1296$

Analyzing Pair 2 (10 : 2160):

Let us test if the same constant multiplier of 216 applies to the second pair:

$10\times 216=2160$

The pattern is verified: each number in the analogy is multiplied by 216 to get the corresponding value.

Finding the missing number (8 : ?):

Applying the exact same rule to 8:

$8\times 216=1728$

Therefore, the number that completes the analogy is 1728.