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Which expression is a perfect cube?

Which expression is a perfect cube?-example-1

2 Answers

3 votes

Answer:

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.

User Marek Stejskal
by
7.8k points
5 votes

Answer:

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)

User Welgriv
by
8.3k points

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