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\(-27x^9+y^6 = (-3)^3\times \Big(x^3\Big)^3 + \Big(y^2\Big)^3=\boxed{\Big(-3x^3\Big)^3+\Big(y^2\Big)^3}\)

Answer:

Option (3) is correct.

\(-27x^9+y^6\) is the expression written as the sum of cubes as

\((-3x^3)^3+(y^2)^3\)

Step-by-step explanation:

Sum of cubes : is defined as  \(a^3+b^3\)

We have to choose a sum of cubes from given expressions,

Consider \(-27x^9+y^6\)

Here  \(-27x^9\) can be written as \((-3x^3)^3\)

and \(y^6\) can be written as \((y^2)^3\)

Thus, \(-27x^9+y^6=(-3x^3)^3+(y^2)^3\)

Hence, \(-27x^9+y^6\) is the expression written as the sum of cubes as \((-3x^3)^3+(y^2)^3\)

Thus, option (3) is correct.

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