Question

`(16 xx 10^2 xx 64)/(2^4 xx 4^2)`

Answer 1

Using laws of exponents,

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

∴ `(16 xx 10^2 xx 64)/(2^4 xx 4^2) = (4)^2 xx 10^2 xx 2^-4 xx (4)^3 xx 4^-2`  ...`[(∵ 64 = 4 xx 4 xx 4),(and 16 = 4 xx 4)]`

= (4)³ × 10² × 2^–4

= (2²)³ × 10² × 2^–4

= 2⁶ × 10² × 2^–4

= 2² × 10²  ...[∵ 2² = 4]

= 4 × 100

= 400