Question

What will come in place of question mark (?) in the following question?

(-1/27)(-1/9) ÷ (1/3)⁵(-1/3)⁴ = ?

1. 27
2. 243
3. 9
4. 81

Answer 1

Correct Answer - Option 4 : 81

Given:

(-1/27)(-1/9) ÷ (1/3)⁵(-1/3)⁴ = ?

Concept used:

a^m × aⁿ = a^{m + n}

a^m ÷ aⁿ = a^{m – n}

Calculation:

(-1/27)(-1/9) ÷ (1/3)⁵(-1/3)⁴ = ?

⇒ (1/3)³(1/3)² ÷ [(1/3)⁵(1/3)⁴] = ?

⇒ (1/3)^{3 + 2} ÷ (1/3)^{5 + 4} = ?

⇒ 1/3⁵ ÷ 1/3⁹ = ?

⇒ 3^{- 5} ÷ 3^{- 9} = ?

⇒ 3^{[- 5 – (- 9)]} = ?

⇒ 3^{(– 5 + 9)} = ?

⇒ 3⁴ = ?

⇒ 81 = ?

∴ The value of ‘?’ is 81.