Question

A number $a$ is called a perfect cube if there exists a natural number $b$ such that:

• A. $a=b\times b\times b$
• B. $b=a\times a\times a$
• C. $a=a\times b\times a$
• D. $a=a\times b\times b$

Answer 1

The correct option is A $a=b\times b\times b$

Given, $a=b\times b\times b$.

Then, $a$ is a perfect cube if $a=b^3$.

We know, a perfect cube has multiples of $3$ as powers of prime factors.
Then clearly, option $A$ is correct.