A positive integer is a perfect power if there exist integers such that and . In particular, is said to be a perfect th power. For example, , so is a perfect nd, rd and th power.
We restrict only because "being a perfect st power" is a meaningless property: every integer is a st power of itself.
Perfect second powers are also known as perfect squares and perfect third powers are also known as perfect cubes. This is because the area of a square and the volume of a cube is equal to the second and third powers of a side length, respectively.