Question

On multiplying ______ by 2^–5 we get 2⁵.

Answer 1

On multiplying 2¹⁰ by 2^–5 we get 2⁵.

Explanation:

Let x be multiplied by 2^–5 to get 2⁵.

So, x × 2^–5 = 2⁵

⇒ `x xx 1/2^5 = 2^5`  ...`[∵ a^-m = 1/a^m]`

∴ x = 2⁵ × 2⁵

= (2)^{5 + 5}  ...[∵ a^m × aⁿ = (a)^{m + n}]

= 2¹⁰