page_title: Perfect power
hierarchical_section_title: Perfect power
caption_attribution_description: English: Showing, through Cuisenaire rods, that 4, 8, and 9 are perfect power numbers.
context_page_description: In mathematics, a perfect power is a positive integer that can be resolved into equal factors, and whose root can be exactly extracted. i.e., a positive integer that can be expressed as an integer power of another positive integer. More formally, n is a perfect power if there exist natural numbers m > 1, and k > 1 such that mᵏ = n. In this case, n may be called a perfect kth power. If k = 2 or k = 3, then n is called a perfect square or perfect cube, respectively. Sometimes 0 and 1 are also considered perfect powers.
context_section_description: In mathematics, a perfect power is a positive integer that can be resolved into equal factors, and whose root can be exactly extracted. i.e., a positive integer that can be expressed as an integer power of another positive integer. More formally, n is a perfect power if there exist natural numbers m > 1, and k > 1 such that mᵏ = n. In this case, n may be called a perfect kth power. If k = 2 or k = 3, then n is called a perfect square or perfect cube, respectively. Sometimes 0 and 1 are also considered perfect powers (0ᵏ = 0 for any k > 0, 1ᵏ = 1 for any k).
caption: Demonstration, with Cuisenaire rods, of the perfect power nature of 4, 8, and 9
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