X^n -27 is divisible by x-3 when n is equal to
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xⁿ - 27 is divisible by (x - 3)
∴ (xⁿ - 3³) is divisible by (x - 3)
∴ (x - 3) is a factor of xⁿ - 3³
∴ x = 3 is a root of xⁿ - 27
So, put x = 3 in expression (xⁿ - 3³)
3ⁿ - 3³ = 0
⇒ 3ⁿ = 3³
⇒ n = 3
Hence, answer is n = 3
∴ (xⁿ - 3³) is divisible by (x - 3)
∴ (x - 3) is a factor of xⁿ - 3³
∴ x = 3 is a root of xⁿ - 27
So, put x = 3 in expression (xⁿ - 3³)
3ⁿ - 3³ = 0
⇒ 3ⁿ = 3³
⇒ n = 3
Hence, answer is n = 3
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