The following is a list of perfect squares.

1² = 1
2² = 4
3² = 9
4² = 16
5² = 25
6² = 36
7² = 49
8² = 64
9² = 81
10² = 100
11² = 121
12² = 144

If a variable with an exponent has an even exponent then it is a perfect square. To get the square root, we simply divide the exponent by 2. For example x⁸ is a perfect square, its square root is x⁴ . x¹¹ is not a perfect square.

The following is a list of perfect Cubes

1³ = 1
2³ = 8
3³ = 27
4³ = 64
5³ = 125
6³ = 216
7³ = 343
8³ = 512
9³ = 729
10³ = 1000

If a variable with an exponent has an exponent which is divisible by 3 then it is a perfect cube. To get the cube root, we simply divide the exponent by 3. For example x⁹ is a perfect cube, its cube root is x³ . x¹¹ is not a perfect cube.