Question

Simplify:

`(3^5 xx 10^5 xx 25)/(5^7 xx 6^5)`

Answer 1

`(3^5 xx 10^5 xx 25)/(5^7 xx 6^5)`

= `(3^5 xx (2 xx 5)^5 xx 5 xx 5)/(5^7 xx 2^5 xx 3^5)`

= `(3^5 xx 2^5 xx 5^5 xx 5^2)/(5^7 xx 2^5 xx 3^5)`       ...[∵ (a × b)^m = a^m × b^m]

= `(3^5 xx 2^5 xx 5^(5  +  2))`          ...[∵ a^m × aⁿ = a^{m + n}]

= `(3^5 xx 2^5 xx 5^7)/(5^7 xx 2^5 xx 3^5)`

= 3^{5 - 5} × 2^{5 - 5} × 5^{7 - 7}        ...[∵ a^m ÷ aⁿ = a^{m - n}]

= 3⁰ × 2⁰ × 5⁰

= 1 × 1 × 1

= 1