What will come in place of the question mark ‘?’ in the following question?
(4 × 4)³ ÷ (512 ÷ 8)⁴ × (32 × 8)⁴ = (2 × 2)^{(? + 4)}

Question

Question

Answer 1

Concept used:

ax × ay = ax + y

ax ÷ ay = ax - y

BODMAS

Calculation:

(4 × 4)³ ÷ (512 ÷ 8)⁴ × (32 × 8)⁴ = (2 × 2)^{(? + 4)}

⇒ 4⁶ ÷ (64)⁴ × 256⁴= (4)^{(? + 4)}

⇒ 4⁶ ÷ (4³)⁴ × (4⁴)⁴ = (4)^{(? + 4)}

⇒ 4^{(6 + 16 - 12)} = (4)^{(? + 4)}

⇒ 4¹⁰ = (4)^{(? + 4)}

So, ? + 4 = 10

⇒ ? = 10 - 4

∴ ? = 6