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

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

Answer 2

Answer:  Second option is correct.

Step-by-step 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.