Question

Find the value of n.

`(2^n xx 2^6)/2^-3 = 2^18`

Answer 1

Given, `(2^n xx 2^6)/2^-3 = 2^18`

Using law of exponents,

`a^-m = 1/a^m`  ...[∵ a is non-zero integer]

⇒ 2ⁿ × 2⁶ × 2³ = 2¹⁸

⇒ 2^{n + 9} = 2¹⁸   ...[∵ a^m × aⁿ = a^{m + n}]

On comparing both sides, we get   

n + 9 = 18  ...[∵ a^m ÷ aⁿ = (a)^{m – n}]

⇒ n = 9