Question

Which expression is a perfect cube?

Answer 1

Answer:

Only $y^{24}$ is a perfect cube.

Step-by-step 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  

$y^{24} =y^{8+8+8}= y^{8} \times y^{8} \times y^{8}= (y^{8}) ^{3}$  

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)

Answer 2

Answer:

Option B.

Step-by-step 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.

$y^{24}=y^{8\times 3}=(y^8)^3$        $[\because (x^m)^n=x^{mn}]$

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.