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The value of \(\dfrac{{{3^{ - 5}} \times {9^{ - 5}}}}{{{{27}^{ - 2}} \times {{243}^{ - 2}}}} = \) ______
1. 3
2. 6
3. 9
4. 27

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Correct Answer - Option 1 : 3

Concept Used:

Law of indices:

(am)n = amn

1/am = a- m

am × an = am + n

Calculation:

⇒ ? = (3- 5  × 9- 5)/(27- 2 × 243- 2)

⇒ ? = (3- 5 × 3(- 5 × 2))/(3(- 2 × 3) × 3(- 2 × 5))

⇒ ? = 3(- 15)/3(- 16)

⇒ ? = 3(-15 + 16)

⇒ ? = 31 = 3

∴ The required value is 3

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