Question

सरल कीजिए -

`((3^-2)^2 xx (5^2)^-3 xx (t^-3)^2)/((3^-2)^5 xx (5^3)^-2 xx (t^-4)^3`

Answer 1

दिया गया है, `((3^-2)^2 xx (5^2)^-3 xx (t^-3)^2)/((3^-2)^5 xx (5^3)^-2 xx (t^-4)^3`

= `((3)^-4 xx (5)^-6 xx (t)^-6)/((3)^-10 xx (5)^-6 xx (t)^-12)`  ...[∵ a^–m × (a)^mn]

= `(3)^-4 × (3)^10 × (5)^-6 × (5)^6 × (t)^-6 × (t)^12`

= `(3)^(-4 + 10) xx (5)^(-6 + 5) xx (t)^(-6 + 12)`  ...`[∵ a^-m = 1/a^m]`

= (3)⁶ × 5⁰ × (t)⁶  ...[∵ a⁰ = 1]

= (3t)⁶