Question

Which expression is a perfect cube?

Answer 1

Option B.

Explanation:

We need to find the expression that is a perfect cube.

First expression is
`x^8`. The degree of x is 8 which is not divisible by 3. So,
`x^8` is not a perfect cube.

Second expression is
`y^(24)`. The degree of y is 24 which is divisible by 3.

`y^(24)=y^(8* 3)=(y^8)^3`
`[\because (x^m)^n=x^(mn)]`

So,
`y^(24)` is a perfect cube.

Third expression is
`m^(28)`. The degree of m is 28 which is not divisible by 3. So,
`m^(28)` is not a perfect cube.

Fourth expression is
`s^(64)`. The degree of s is 64 which is not divisible by 3. So,
`s^(64)` is not a perfect cube.

Therefore, the correct option is B.

Answer 2

Only
`y^(24)` is a perfect cube.

Explanation:

`x^(8)` is not a perfect cube because 8 is not a multiple of 3.

Now,
`y^(24)` is a perfect cube since 24 is a multiple of 3.

So,
`y^(24)` can be expressed as

`y^(24) =y^(8+8+8)= y^(8) * y^(8) * y^(8)= (y^(8)) ^(3)`

Again,
`m^(28)` is not a perfect cube as 28 is not a multiple of 3.

And also
`s^(64)` is not a perfect cube as 64 is not a multiple of 3.

Therefore, only
`y^(24)` is a perfect cube. (Answer)