Final answer:
After evaluating, none of the lists provided contain only integers, as all have terms that are either decimal numbers or roots of non-perfect squares, which do not result in integers. Understanding integers and integer powers is key to solving such questions.
Step-by-step explanation:
When we are asked to identify which list contains only integers, it is important to understand what an integer is. An integer is a whole number that can be positive, negative, or zero, but it cannot be a fraction or include a decimal point with a non-zero fractional part. Given the lists provided, we aim to find the one with only integers.
Looking at the lists within the question:
- 6.0, 5√, 90
- 279, 4√, -4
- −√81, -7, 45
- 4³, 64√, 5.321...
We can determine the property of each term:
- 6.0 is an integer because it represents 6 without any fractional part.
- The second term in every list is a root, which may or may not be an integer.
- Look for non-integer terms or roots that do not simplify to integers.
- Lastly, evaluate which list exclusively accommodates integers.
From this evaluation, the list containing
-81, -7, 45
includes only integers, presuming the '−√' prior to '81' signifies the square root of -81, which is a complex number (not an integer), making this a trick question. If the symbol is meant to be a subtraction, then the list would be valid, as -81, -7, and 45 are all integers. Assuming the correct list should contain only integers and not involve complex numbers, none of the provided lists are correct. Every list either includes a decimal that is not 0 or involves the square root of a number that is not a perfect square, which doesn't result in an integer.