Question

`(125 xx x^-3)/(5^-3 xx 25 xx x^-6)`

Answer 1

Using laws of exponents,

a^m + aⁿ = (a)^{n – m} and `a^-m = 1/a^m`  ...[∵ a is non-zero integer]

∴ `(125 xx x^-3)/(5^-3 xx 25 xx x^-6) = (5)^3 xx 5^3 xx 5^-2 xx x^-3 xx x^6`  ....`[(∵ 125 = 5 xx 5 xx 5),("and"  25 = 5 xx 5)]`

= 5⁴ × x³

= 5 × 5 × 5 × 5 × x³  ...[∵ a^m × aⁿ = a^{m + n}]

= 625 x³