Question

Simplify.

`(3^(-5) xx 10^(-5) xx 125)/(5^(-7) xx 6^(-5))`

Answer 1

`(3^(-5)xx10^(-5)xx125)/(5^(-7)xx6^(-5))`

`=(3^(-5)xx(2xx5)^5xx5^3)/(5^(-7)xx(2xx3)^(-5))`

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

`= 3^(-5-(-5))xx2^(-5-(-5))xx5^(-5+3-(-7))`   ...(a^m ÷ aⁿ = a^m−n)

= 3⁰ × 2⁰ × 5⁵    ...(a⁰ = 1)

= 5⁵