Answer:
Only [tex]y^{24}[/tex] is a perfect cube.
Step-by-step explanation:
[tex]x^{8}[/tex] is not a perfect cube because 8 is not a multiple of 3.
Now, [tex]y^{24}[/tex] is a perfect cube since 24 is a multiple of 3.
So, [tex]y^{24}[/tex] can be expressed as
[tex]y^{24} =y^{8+8+8}= y^{8} \times y^{8} \times y^{8}= (y^{8}) ^{3} [/tex]
Again, [tex]m^{28}[/tex] is not a perfect cube as 28 is not a multiple of 3.
And also [tex]s^{64}[/tex] is not a perfect cube as 64 is not a multiple of 3.
Therefore, only [tex]y^{24}[/tex] is a perfect cube. (Answer)
Answer:
Option B.
Step-by-step explanation:
We need to find the expression that is a perfect cube.
First expression is [tex]x^8[/tex]. The degree of x is 8 which is not divisible by 3. So, [tex]x^8[/tex] is not a perfect cube.
Second expression is [tex]y^{24}[/tex]. The degree of y is 24 which is divisible by 3.
[tex]y^{24}=y^{8\times 3}=(y^8)^3[/tex] [tex][\because (x^m)^n=x^{mn}][/tex]
So, [tex]y^{24}[/tex] is a perfect cube.
Third expression is [tex]m^{28}[/tex]. The degree of m is 28 which is not divisible by 3. So, [tex]m^{28}[/tex] is not a perfect cube.
Fourth expression is [tex]s^{64}[/tex]. The degree of s is 64 which is not divisible by 3. So, [tex]s^{64}[/tex] is not a perfect cube.
Therefore, the correct option is B.
