Question

Which expression is a perfect cube?

-1452m^18n^15p^22
-1331m^18n^15p^21
1331m^18n^15p^22
1452m^18n^15p^21

Answer 1

Let's start with coefficient.

Note that 11³ = 1331 and 12³ = 1728
and (-11)³ = -1331 and (-12)³ = -1728

So -1452 and 1452 cannot be perfect cube.

We are left with B or C.

Now check for exponent of p.

p²¹ has exponent multiple of 3 which makes it perfect cube

The exponent of p²² is not multiple of 3 so it's not perfect cube.

So final answer: B) -1331 m¹⁸ n¹⁵ p²¹