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In the prime factorisation of a perfect cube, how many times must each prime factor occur (or a multiple of how many)?

Class 8Cube Root by Prime FactorisationCubes and Roots
  • Aa multiple of 3
  • Ba multiple of 2
  • Cexactly once
  • Da multiple of 4

Step-by-Step Solution

A perfect cube has every prime appearing in groups of three, i.e. the exponent of each prime is a multiple of 3.
Answer: A) a multiple of 3

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