Question

Which expression is a perfect cube?

A:12x^12 y^18
B:12x^27 y^125
C:64x^15 y^18
D:64x^27 y^125

Answer 1

we know that

A perfect cube is a whole number which is the cube of another whole number or a number is a perfect cube if the cube root of that number is a whole number.

so

case a)
`12x^(12) y^(18)`

`12x^(12) y^(18) = 12(x^(4) y^(6))^(3)`

the cube root of
`12` is not a whole number

therefore

The expression is not a perfect cube

case b)
`12x^(27) y^(125)`

`12x^(27) y^(125) = 12(x^(9))^(3)y^(125)`

the cube root of
`12` is not a whole number

the cube root of
`y^(125)` is not a whole number

therefore

The expression is not a perfect cube

case c)
`64x^(15) y^(18)`

`64x^(15) y^(18) = (4 x^(5) y^(6))^(3)`

therefore

The expression is a perfect cube

case d)
`64x^(27) y^(125)`

`64x^(27) y^(125) = (4 x^(9))^(3)y^(125)`

the cube root of
`y^(125)` is not a whole number

therefore

The expression is not a perfect cube

the answer is

`64x^(15) y^(18)`