Question

Which expression is a perfect cube? -1,452m^18n^15p^22, -1,331m^18 n^15p^21, 1,331m^18n^15p^22, 1,452m^18n^15p^21

Answer 1

Answer: Second option is correct.

Explanation:

Since we have given that

`-1,452m^(18)n^(15)p^(22)\\\\ -1,331m^(18) n^(15)p^(21),\\\\1,331m^(18)n^(15)p^(22),\\\\ 1,452m^(18)n^(15)p^(21)`

we need to find the perfect cube.

As we know that

1331 is the cube of 11

and 18 is multiple of 3

15 is also a multiple of 3

21 is also a multiple of 3.

So, we can write it as

`-1331m^(18)n^(15)p^(21)=(-11m^6n^5p^7)^3`

So, it is a perfect cube.

Hence, Second option is correct.

Answer 2

An expression is said to be a perfect cube if the expression is as a result of raising another expression to the power of 3.

An exponent can be expressed as a perfect cube if the exponent is divisible by 3.

Therefore, the expression that is a perfect cube is

`-1,331m^(18) n^(15)p^(21)=\left(-11m^6n^5p^7\right)^3`