Verified Answer :

When a number is multiplied by itself three times, then the resultant number is called a perfect cube. It is also a number with an exact cube root.

Out of the given options, \(8x^{12}\) and \(27x^{9}\) are perfect cubes.

\(8x^{12}\) = \(2x^{4}\times 2x^{4}\times 2x^{4}\) (2's are multiplied and powers are added)

\(27x^{9}\) = \(3x^{3}\times 3x^{3}\times 3x^{3}\) (3's are multiplied and powers are added)

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The monomials that are perfect cubes out of the options given are: B. 8x^12, and C. 27x9.

What is a Perfect Cube?

A perfect cube is a number that can give you a precise cube root, i.e. a³ = a × a × a = ∛a³ = a.

27x^9 can be expressed as: ∛(27x^9) = 3x³

8x^12 can be expressed as: ∛(8x^12) = 2x^4

Therefore, the perfect cubes are: B. 8x^12, and C. 27x9.

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