Square of a non zero perfect cube will also be a perfect cube true or false 

The statement "The square of a non-zero perfect cube will also be a perfect cube" is **false**.

### Explanation:
- A perfect cube is a number of the form \( n^3 \) where \( n \) is an integer.
- The square of a perfect cube \( n^3 \) is \( (n^3)^2 = n^6 \).

For \( n^6 \) to be a perfect cube, \( n^6 \) must be expressible as \( m^3 \) for some integer \( m \). This implies:
\[
n^6 = m^3 \Rightarrow (n^2)^3 = m^3 \Rightarrow n^2 = m
\]
This means \( n^6 \) is only a perfect cube if \( n \) is already a perfect square. In general, not all integers \( n \) are perfect squares, so the square of a non-zero perfect cube is not necessarily a perfect cube.

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### Related Questions:
1. What is a perfect square? Provide examples.
2. If \( n \) is a perfect square, is \( n^3 \) also a perfect cube?
3. Can a number be both a perfect square and a perfect cube? Provide examples.
4. What are the properties of perfect powers, such as cubes and squares?
5. How can you determine if a large number is a perfect cube?

**Tip:** When working with exponents, always consider the relationship between the base and the exponent to determine the properties of the resulting number.

Explore whether the square of a non-zero perfect cube is also a perfect cube with a detailed explanation. Understand the concept of perfect cubes and exponents in mathematics. Suitable for high school students and anyone interested in advanced mathematical concepts.

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