Question

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

100² × 10³ ÷ 1000 × 10000³ ÷ 100000 × 1000000 = 10^?

1. 18
2. 17
3. 16
4. 15

Answer 1

Correct Answer - Option 2 : 17

Given:

100² × 10³ ÷ 1000 × 10000³ ÷ 100000 × 1000000 = 10^?

Concept used:

a^m × aⁿ ÷ a^p = a^{(m + n – p)}

Calculation:

100² × 10³ ÷ 1000 × 10000³ ÷ 100000 × 1000000 = 10^?

⇒ (10)^{2 × 2} × (10)³ ÷ (10)³ × (10)^{4 × 3} ÷ (10)⁵ × (10)⁶ = 10^?

⇒ (10)⁴ × (10)³ ÷ (10)³ × (10)¹² ÷ (10)⁵ × (10)⁶ = 10^?

⇒ (10)^{(4 + 3 – 3 + 12 – 5 + 6)} = 10^?

⇒ (10)^{(25 – 8)} = 10^?

⇒ (10)¹⁷ = 10^?

⇒ ? = 17

∴ The value of ‘?’ is 17.