Question

Each prime factor appears 3 times in its cube. State whether the statement is true (T) or false (F).

• A. True
• B. False

Answer 1

The correct option is A True

Solution:

A perfect cube can always be expressed as the product of triplets of prime factors. Every number can be expressed as the product of the power of its Prime factors. If the power of all the Prime factors is in the multiple of $3$, then the number is said to be a perfect cube.

For instance,

${15}^3=15\times 15\times 15=3\times 5\times 3\times 5\times 3\times 5=3^3\times 5^3$

Hence, the given statement is True