Answer:
- squares: 1, 36, 64, 289, 324
- cubes: 1, 64, 125, 216, 512
Explanation:
You want lists of the perfect squares and perfect cubes from the set {1, 36, 64, 98, 125, 216, 289, 324, 480, 512}.
Perfect squares
A "perfect square" is the square of an integer, the value obtained by multiplying the integer by itself.
Squares of numbers 1–10 are ...
1, 4, 9, 16, 25, 36, 49, 64, 81, 100
And from 11–20:
121, 144, 169, 196, 225, 256, 289, 324, 361, 400
The squares on your list are 1, 36, 64, 289, 324.
Perfect cubes
A "perfect cube" is the cube of an integer, the value obtained by using the value 3 times as a factor in a product. (n³ = n×n×n)
Cubes of numbers 1–10 are ...
1, 8, 27, 64, 125, 216, 343, 512, 729, 1000
The cubes on your list are 1, 64, 125, 216, 512.
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Additional comment
Any integer to the 6th power will be both a perfect square and a perfect cube. The integers 1 = 1⁶, 64 = 2⁶, and 729 = 3⁶ are such numbers.