Question

Simplify:

(2⁵ ÷ 2⁸) × 2^–7

Answer 1

Using laws of exponents, a^m ÷ aⁿ = (a)^{m – n} and a^m × aⁿ = (a)^{m + n}  ...[∵ a is non-zero integer]

∴ (2⁵ ÷ 2⁸) × (2)^–7 = (2)^{5 – 8} × (2)^–7

= (2)^–3 × (2)^–7

= (2)^{–3 – 7}

= (2)^–10

= `1/2^10`  ...`[∵ a^-m = 1/a^m]`

= `1/1024`