If 324 × 918 = 27k, then what is the value of k?1. 152. 203. 184. 16

1.	If 324 × 918 = 27k, then what is the value of k?1. 152. 203. 184. 16
Answer» Correct Answer - Option 2 : 20 Given: 324 × 918 = 27^k Formula used: (am)n = amn am × an = am + n am = an ⇒ m = n Calculations: 27 = 3³ 9 = 3² ⇒ 3²⁴ × (3²)⁽¹⁸⁾= (3)^3k----(∵ (a^m)ⁿ = a^mn) ⇒ 3^{(24 + 36)}= 3^3k----(∵ a^m × aⁿ = a^{m + n}) ⇒ 3⁶⁰ = 3^3k ----(∵ a^m = aⁿ⇒ m = n) ⇒ 3k = 60 ⇒ k = 20 ∴ The value of k is 20

Answer» Correct Answer - Option 2 : 20

Given:

324 × 918 = 27^k

Formula used:

(am)n = amn

am × an = am + n

am = an ⇒ m = n

Calculations:

27 = 3³

9 = 3²

⇒ 3²⁴ × (3²)⁽¹⁸⁾= (3)^3k----(∵ (a^m)ⁿ = a^mn)

⇒ 3^{(24 + 36)}= 3^3k----(∵ a^m × aⁿ = a^{m + n})

⇒ 3⁶⁰ = 3^3k ----(∵ a^m = aⁿ⇒ m = n)

⇒ 3k = 60

⇒ k = 20

∴ The value of k is 20

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